{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 最小二乘法Least Squred and Mathematical Tools"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np  # 引入numpy\n",
    "import scipy as sp\n",
    "import pylab as pl\n",
    "from scipy.optimize import leastsq  # 引入最小二乘函数\n",
    "n = 9  # 多项式次数\n",
    "# 目标函数\n",
    "def real_func(x):\n",
    "    return np.sin(2 * np.pi * x)\n",
    "# 多项式函数\n",
    "def fit_func(p, x):\n",
    "    f = np.poly1d(p)\n",
    "    return f(x)\n",
    "\n",
    "# 残差函数\n",
    "def residuals_func(p, y, x):\n",
    "    ret = fit_func(p, x) - y\n",
    "    return ret\n",
    "\n",
    "# 残差函数\n",
    "def residuals_func1(p, y, x):\n",
    "    ret = fit_func(p, x) - y\n",
    "    ret = np.append(ret, np.sqrt(regularization) * p) \n",
    "  # 将lambda^(1/2)p加在了返回的array的后面\n",
    "    return ret\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Fitting Parameters:  [-5.86405699e+00  7.94723345e-02  5.27211548e+00  7.89157120e+00\n",
      "  5.24080573e+00 -4.68525348e+00 -1.54817346e+01  7.67992286e+00\n",
      " -9.80580778e-03]\n"
     ]
    }
   ],
   "source": [
    "x = np.linspace(0, 1, 9)  # 随机选择9个点作为x\n",
    "x_points = np.linspace(0, 1, 1000)  # 画图时需要的连续点\n",
    "\n",
    "y0 = real_func(x)  # 目标函数\n",
    "y1 = [np.random.normal(0, 0.1) + y for y in y0]  # 添加正太分布噪声后的函数\n",
    "p_init = np.random.randn(n)  # 随机初始化多项式参数\n",
    "\n",
    "regularization = 0.0001  # 正则化系数lambda    \n",
    "#regularization = 0.1  # 正则化系数lambda    Bad for  it \n",
    "plsq = leastsq(residuals_func1, p_init, args=(y1, x))\n",
    "\n",
    "print ('Fitting Parameters: ', plsq[0])  # 输出拟合参数\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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k/HfPh8QYxl7qxlP3VpPB2+yBRyno8A4VkyIZ6L6JCbL2L+yQfZe/yYReP5Fj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\nAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fe0ec48e358>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pl.plot(x_points, real_func(x_points), label='real')\n",
    "pl.plot(x_points, fit_func(plsq[0], x_points), label='fitted curve')\n",
    "pl.plot(x, y1, 'bo', label='with noise')\n",
    "pl.legend()\n",
    "pl.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Fitting Parameters:  [ 4.27685970e+03 -1.71266916e+04  2.81408447e+04 -2.44786676e+04\n",
      "  1.21192016e+04 -3.37979151e+03  4.67148368e+02 -1.87660052e+01\n",
      " -1.78225226e-02]\n"
     ]
    }
   ],
   "source": [
    "regularization = 0.1  # 正则化系数lambda\n",
    "plsq = leastsq(residuals_func, p_init, args=(y1, x))\n",
    "\n",
    "print ('Fitting Parameters: ', plsq[0])  # 输出拟合参数"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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2X+4Kxse9JoNa1S26YHoSXD8GjfuVXXCKpv/HUKcNrH+VOuIOr/ZqzI6Lt/AP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\n+2wxNgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fe0edde1e80>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pl.plot(x_points, real_func(x_points), label='real')\n",
    "pl.plot(x_points, fit_func(plsq[0], x_points), label='fitted curve')\n",
    "pl.plot(x, y1, 'bo', label='with noise')\n",
    "pl.legend()\n",
    "pl.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Approximation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'/home/lab466/pythons/py4fiYves/ipython'"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "##########From py4fiYves/003_Financial_LS \n",
    "import os\n",
    "os.chdir(\"/home/lab466/pythons/py4fiYves/ipython\")\n",
    "os.getcwd()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true,
    "uuid": "460b709e-eed1-48e4-b3ad-d07377ea5de6"
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true,
    "uuid": "2326c3ad-f244-4f48-8b68-851bd2347d57"
   },
   "outputs": [],
   "source": [
    "def f(x):\n",
    "    return np.sin(x) + 0.5 * x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": true,
    "uuid": "c09f73d2-c2a5-4c6d-a2f1-08a191378417"
   },
   "outputs": [],
   "source": [
    "x = np.linspace(-2 * np.pi, 2 * np.pi, 50)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "uuid": "96d2bd1b-8883-486d-920d-b610aeb076a8"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x7fe0b172a438>"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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SfSoIKcOHQ0UFXHdd7CQiInGoIABLljTlttvgjDNg991jpxERiUMFARg3rjON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\nsR/3hHSN70cAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fe0b17b4b70>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x, f(x), 'b')\n",
    "plt.grid(True)\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('f(x)')\n",
    "# tag: sin_plot\n",
    "# title: Example function plot\n",
    "# size: 60"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Least Squared and Regression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Monomials as Basis Functions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": true,
    "uuid": "ace90420-7219-4227-8210-bf107f556726"
   },
   "outputs": [],
   "source": [
    "reg = np.polyfit(x, f(x), deg=1)\n",
    "ry = np.polyval(reg, x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "uuid": "c0667d3e-a48a-413d-b250-5e0d3b58275e"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x7fe0b188be80>"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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RQAlBRESKKSF4k4IOIEphjx/Cfw5hjx/Cfw5hjx8CPgf1IYiICKA7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\nIYiISDElBBERAeD/A0MV7wIdmaLVAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fe0b169e780>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x, f(x), 'b', label='f(x)')\n",
    "plt.plot(x, ry, 'r.', label='regression')\n",
    "plt.legend(loc=0)\n",
    "plt.grid(True)\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('f(x)')\n",
    "# tag: sin_plot_reg_1\n",
    "# title: Example function and linear regression\n",
    "# size: 60"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": true,
    "uuid": "096bb07a-55f7-45de-8734-2a76d8749d53"
   },
   "outputs": [],
   "source": [
    "reg = np.polyfit(x, f(x), deg=5)\n",
    "ry = np.polyval(reg, x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "uuid": "5e17309e-e8e2-4df9-b841-0f57d983b89e"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x7fe0b16b87b8>"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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7D95/H158EfLygg5QJFjOzNJzYuemAVsneOtiM3s6fkwMGG1mcxIcV3meYcAw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\nQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fe0b15cd0b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x, f(x), 'b', label='f(x)')\n",
    "plt.plot(x, ry, 'r.', label='regression')\n",
    "plt.legend(loc=0)\n",
    "plt.grid(True)\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('f(x)')\n",
    "# tag: sin_plot_reg_2\n",
    "# title: Regression with monomials up to order 5\n",
    "# size: 60"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": true,
    "uuid": "67b14a21-e8f2-4dd4-a43b-0d232f2b4055"
   },
   "outputs": [],
   "source": [
    "reg = np.polyfit(x, f(x), 7)\n",
    "ry = np.polyval(reg, x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "uuid": "053752b7-7eb3-4d93-acdf-69874ceada12"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x7fe0b1557ac8>"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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U5smQkYisBTB6G4fy2MaNMPQJi0HHh3n0AhvyQlqiQqUsnUNQKW3UKCgpgVFz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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fe0b158abe0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x, f(x), 'b', label='f(x)')\n",
    "plt.plot(x, ry, 'r.', label='regression')\n",
    "plt.legend(loc=0)\n",
    "plt.grid(True)\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('f(x)')\n",
    "# tag: sin_plot_reg_3\n",
    "# title: Regression with monomials up to order 7\n",
    "# size: 60"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "uuid": "e600b6be-4cf2-4212-807a-7f397f081e98"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "False"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.allclose(f(x), ry)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "uuid": "bc6918fe-f520-483c-94eb-41dd89abfa70"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0017769134759517584"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.sum((f(x) - ry) ** 2) / len(x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Individual Basis Functions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": true,
    "uuid": "b4f05890-56e0-4f29-9d61-bd9948ad8af0"
   },
   "outputs": [],
   "source": [
    "matrix = np.zeros((3 + 1, len(x)))\n",
    "matrix[3, :] = x ** 3\n",
    "matrix[2, :] = x ** 2\n",
    "matrix[1, :] = x\n",
    "matrix[0, :] = 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "uuid": "c8963eee-4bc8-4ef2-a172-d4b64fd065a3"
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/lab466/anaconda3/lib/python3.6/site-packages/ipykernel_launcher.py:1: FutureWarning: `rcond` parameter will change to the default of machine precision times ``max(M, N)`` where M and N are the input matrix dimensions.\n",
      "To use the future default and silence this warning we advise to pass `rcond=None`, to keep using the old, explicitly pass `rcond=-1`.\n",
      "  \"\"\"Entry point for launching an IPython kernel.\n"
     ]
    }
   ],
   "source": [
    "reg = np.linalg.lstsq(matrix.T, f(x))[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "uuid": "efd077d1-9c8a-4961-be95-400f83cd679e"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1.16778801e-14,  5.62777448e-01, -8.88178420e-16, -5.43553615e-03])"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "reg"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": true,
    "uuid": "efb7b252-d0f8-4263-b2be-4d9588ab06a7"
   },
   "outputs": [],
   "source": [
    "ry = np.dot(reg, matrix)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "uuid": "1b1953fe-83a2-436b-8cd4-69c5abf6d2e1"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x7fe0b14dbcf8>"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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LoXPnKp9OJHSUECScItB5XNTNN/tagRawk5pKTUYS/8q5m1lVLFgATz/t+w9a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\nAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fe0b144ef60>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x, f(x), 'b', label='f(x)')\n",
    "plt.plot(x, ry, 'r.', label='regression')\n",
    "plt.legend(loc=0)\n",
    "plt.grid(True)\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('f(x)')\n",
    "# tag: sin_plot_reg_4\n",
    "# title: Regression via least-squares function\n",
    "# size: 60"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "uuid": "ac77ef01-8abe-4b99-8f92-8325a396ff2c"
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/lab466/anaconda3/lib/python3.6/site-packages/ipykernel_launcher.py:2: FutureWarning: `rcond` parameter will change to the default of machine precision times ``max(M, N)`` where M and N are the input matrix dimensions.\n",
      "To use the future default and silence this warning we advise to pass `rcond=None`, to keep using the old, explicitly pass `rcond=-1`.\n",
      "  \n"
     ]
    }
   ],
   "source": [
    "matrix[3, :] = np.sin(x)\n",
    "reg = np.linalg.lstsq(matrix.T, f(x))[0]\n",
    "ry = np.dot(reg, matrix)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "uuid": "58d9db31-5885-4fba-8ae7-2e962a0963ca"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x7fe0b1792b00>"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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ISGoObMwcYL+dPDVSRF5KvsYGrhORhbs4ziBgEEBOTk7uzJkzazzWoqIiGjVq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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fe0b1409240>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x, f(x), 'b', label='f(x)')\n",
    "plt.plot(x, ry, 'r.', label='regression')\n",
    "plt.legend(loc=0)\n",
    "plt.grid(True)\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('f(x)')\n",
    "# tag: sin_plot_reg_5\n",
    "# title: Regression using individual functions\n",
    "# size: 60"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "uuid": "02481bd5-c737-46bc-9b90-5554fcad8745"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.allclose(f(x), ry)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "uuid": "6bf80137-3a52-483b-a557-b092bbf23b36"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3.806562016482484e-31"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.sum((f(x) - ry) ** 2) / len(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "uuid": "86f9a92c-600d-4515-b34d-20c9f35a86b0"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([4.36463437e-16, 5.00000000e-01, 0.00000000e+00, 1.00000000e+00])"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "reg"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Noisy Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": true,
    "uuid": "75d3a6a6-a940-4a49-b35d-29f21880ab95"
   },
   "outputs": [],
   "source": [
    "xn = np.linspace(-2 * np.pi, 2 * np.pi, 50)\n",
    "xn = xn + 0.15 * np.random.standard_normal(len(xn))\n",
    "yn = f(xn) + 0.25 * np.random.standard_normal(len(xn))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": true,
    "uuid": "f6f9c05f-1f96-48ee-aaca-f4d80c3d3ac5"
   },
   "outputs": [],
   "source": [
    "reg = np.polyfit(xn, yn, 7)\n",
    "ry = np.polyval(reg, xn)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "uuid": "9a475222-3bfd-4300-951b-94e60792c6da"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x7fe0b183aa58>"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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lC6OFWhoql1Pxpz+mfkOai+ZQL+55n9ncO+mmk+5uSUR6KCGELU/zBVLZsAHW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\nEoKIiCQpIYiICKCEICIiSUoIIiICwP8HrZIS3nl8b0AAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fe0b18d6278>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(xn, yn, 'b^', label='f(x)')\n",
    "plt.plot(xn, ry, 'ro', label='regression')\n",
    "plt.legend(loc=0)\n",
    "plt.grid(True)\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('f(x)')\n",
    "# tag: sin_plot_reg_6\n",
    "# title: Regression with noisy data\n",
    "# size: 60"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Unsorted Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": true,
    "uuid": "8ea85cdb-47f2-4967-b684-7894d9964e76"
   },
   "outputs": [],
   "source": [
    "xu = np.random.rand(50) * 4 * np.pi - 2 * np.pi\n",
    "yu = f(xu)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "uuid": "0034edf5-1cef-4eea-be44-c69103fe6eb2"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[-1.06 -1.23 -3.81 -0.23 -5.99 -3.24  4.54  1.19 -4.37 -5.68]\n",
      "[-1.4  -1.56 -1.29 -0.35 -2.71 -1.52  1.28  1.53 -1.24 -2.27]\n"
     ]
    }
   ],
   "source": [
    "print( xu[:10].round(2))\n",
    "print( yu[:10].round(2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "collapsed": true,
    "uuid": "d7f5f003-1cb8-4432-a8d6-cb4bef1a101a"
   },
   "outputs": [],
   "source": [
    "reg = np.polyfit(xu, yu, 5)\n",
    "ry = np.polyval(reg, xu)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "uuid": "40177962-0363-479c-bdbd-451a4c043060"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x7fe0b17ac278>"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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BsTzwQBa68ooUCCWEdKK03nGS5+29M6vCsJbzHKw30ogeJyU+6+Pr69OvIjfM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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fe0b17c60b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(xu, yu, 'b^', label='f(x)')\n",
    "plt.plot(xu, ry, 'ro', label='regression')\n",
    "plt.legend(loc=0)\n",
    "plt.grid(True)\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('f(x)')\n",
    "# tag: sin_plot_reg_7\n",
    "# title: Regression with unsorted data\n",
    "# size: 60"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Multiple Dimensions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "collapsed": true,
    "uuid": "82b95a7b-9e3e-4dc8-b313-1af775b06b8b"
   },
   "outputs": [],
   "source": [
    "#def fm((x, y)):\n",
    "def fm(*args):\n",
    "    x = args[0][0]\n",
    "    y = args[0][1]    \n",
    "    return np.sin(x) + 0.25 * x + np.sqrt(y) + 0.05 * y ** 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "collapsed": true,
    "uuid": "b03b67ac-f7df-41d1-9dab-1e074e8738fa"
   },
   "outputs": [],
   "source": [
    "x = np.linspace(0, 10, 20)\n",
    "y = np.linspace(0, 10, 20)\n",
    "X, Y = np.meshgrid(x, y)\n",
    "  # generates 2-d grids out of the 1-d arrays\n",
    "Z = fm((X, Y))\n",
    "x = X.flatten()\n",
    "y = Y.flatten()\n",
    "  # yields 1-d arrays from the 2-d grids"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "uuid": "52a91ef7-33c4-4de1-b69b-ea4d740aa252"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.colorbar.Colorbar at 0x7fe0b11f7160>"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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nFosxMDDAhQsXeOGFF/id3/kdzp49Szqd5p/+03/KtWvXePHFFx3t4yd+4if4\nyle+su2xl156iQ996EPcv3+fD33oQ7z00kuOfy/F3qIs8SrU6jovWKJeuNpt22Z6epqZmRnC4TBD\nQ0Oe1oM2yhI3TZOJiQnm5uY4d+5cyUYzTqlUyy4fPUDr7kPLJxBW9S/oZDpPS53iK3UfIul+Ulkp\ntOQakWP95DbaMKfGAYFP1l5K5cul8X33j0kOv8p07xB677Et12soFKqp/K8c0rax334V61tfgXSV\nw1OgmdzUG3R96D1oi84TCjMz3rSyFYEA1lztw2kA7EeTHHnPMVbG0yTe2u4d8Le1YM64sPKFoPn9\nf6nkj0zTdPUZ7+zspKuri4sXL/JTP/VTwObh2Qnve9/7ePjw4bbHvvSlL/Hyyy8D8IlPfIIPfOAD\n/OIv/qLj/ew317WojMv9ayU9Ru6PpJR/ZS/upUS8DDsHlbh1nRf6nNcr4mtra4yOjtLR0cGdO3cY\nGRnZ8yS0WjAMg+9///v09fW5zpYvRzkR19Zm0PIJR2vYCMLxlbr3QtcRxJqzYR1OEPkMwYiGdul5\n7GSy4shUpzRlNzj38BXy+RUWjl7k/sIC2WyWYDBIOBwmn89vuW1rwZ68i/W130cuO3sdcnaQ7hcu\ngwsBN1t6MO560xY1NDiINVF/iZq9vkpbX5Bw/y0W/+hJnLzthQtYU85mkgNErl0ncKT0wJRamr2k\n0+lt2en1HPQXFhbo69ssX+zt7WVhwauZAHtDQtj8+6aT+3b/v5oY7dyreykR34HbGd/lKIh4rROF\n8vk8d+/eJZfLcfnyZaLRKNC4THKvYqSGYXDv3j0SiQRDQ0P09vZ6sm6531sm19CWnVtXUgvit2t0\npxbWEAKRra9NaymEtAnkN7AHzyNHv4ew67ckBBB8dJ+BhYcMXHgBeeEKWc3P4uIiq6urvPnmm1iW\nRVNTE7FYbFuiVEmMHHJlHvOVP0FOOBcs/bmzBN5523VP+cyqR6+zEJDwqLUqQD5HiKI4OUDCndC1\nfvRjZX9WixevUSVm+9Vxsi4ECP+zES1WIl6Ebdvk83lPSsZqnTgmpWR6eprp6WlOnTpFT0/Ptn14\nPVMcvDkYSCmZn5/nwYMHnDy5eQJ2NG3MIWX/FpPvOF7DRiAXZ+suK6PrSM0JbdWQbd34shvY5y5h\nTT1EJL0RHmEZyPkH+Ma+TTQYYaC5gygBOo9dxG7tJmlK4vE409PTpFIpNE2jpbmJDp+kxUjijy8j\n1uYhsYqjglvGAAAgAElEQVTha0ZOOCz38vkIXnye3MqaawG3mjrIfcebmeGhM4NYs95kt2/jcZw8\ntWZhTd91fJn/yFEi166X/XktHhIvZ4n39PQwNzdHX18fc3NzdHd3e7LunqGBHlYi/sxQz4zvctQi\nthsbG4yMjNDW1sbt27dLfoj3o6a7Gul0muHhYUKhEDdv3iQQCLCxseFpBvTObHcAmU3BgvMvZqkH\n6x50AjiKu9e8dlsXpNfRsklEfz9WohXmHnqytqZtHl9ELo0/l6YHYHkcHWgNRWlt60W2dUMwDyuP\nEFOLu7wBlhSYs5OODkKio4fQ0X5IrZEfd+/Gzqa9e59rWDSq/ZL9aJKeWzfZCBqkx5zFxFt/4Acr\nGgm1DEDxsmPbD/7gD/KZz3yGF198kc985jN87GPlvQYHESEEmu+QeQ9q5JkW8UaWjLkR8Xw+z/37\n90mn01WHfhwkES9u8zo0NLStBMXrfZbMTp8edtzBy5Yglxfqb+7S0YeW9CCmXmrtaGxbbbsw8+hh\nP/bgZeS979e3dmv51rAAIpuCuXHEXOVSrqwWRnPQA94/eAG/ZiHScTJWADLOy+UA7FALmbe8ae4S\nOH4Cc9aDaoQK6/PoAbFWP6F332L1G5XrybVIlJYPfrjic2qJiSeTSVpanPUJKObjH/84L7/8MsvL\nyxw9epRPfvKTvPjii/zIj/wIn/70pzl+/Dif//znXa+7ryhL/OmmMON7bm4OXddpa2vzPObjRMSl\nlMzOzjI5OcnJkyc5f/581X0cFHf62toaIyMjZdu81jP7vBQ715NmHmbvO75e+sKIZP0tVoXWuNO9\n6N5d3y6Q6GYa+8J1rLtvle0+V3XtaAvk3QlpKfSNNSr9VW3dhzgzRMBKgwW2lOQeundjZwmV7a3u\nFl9TBNNZb5eaCHe3I+cSYBoEzXl6PvJeFl9+BZkv7bFp+fBH0Kp0VqxlAEqt7vTPfvazJR//6le/\n6nqtg4IAhK4s8aeS4pKxzOPWj/WUPpWjmtjG43FGRkZoaWkp6zovRaNqup2KeD6f5969e2SzWa5e\nvVo2A9br8aa7DgWz98CFW1uuLddvhbd1V7Rm61o7EELLlRdZLbOBODOE+WgGseHOEyDDETQPYvhm\nMIZc393zvIDo6CZy5Ah65klf+LWUhbbm7jWzA2EyHrVY9fX0YE560yim5PodHciF7YmV2uIkve+5\nysrwJPn5Ha+7ptH61/561XVrHYCieqc/Rgj0A5zYJoT4T8BHgUUp5cXHj7UDvw2cAB4CPyKlrFrH\n+syIeCnXuc/nI5dzl2zjlHIibhgGY2NjxONxhoaGXLu/dF3fypz3CicHAyklc3NzTExM8Nxzz9Hb\n21vRa1Aqhl0PxSIubWvTle4QyxdCbHhghQeC4Kz01j19JxC5ymVyIpfC192N1dIK086FSXT0uW4N\nWwozWT6fwH/mAn7dQmS2D3bxxROuY9H5QCsyX/84UIBgTzfGuDf1/KWIPHcS5kp4GlYX6DjRTqqn\ni/ibT5Ivo9dv4u+tPnlOSulaxA3D8DSZ9DAjBOiB+hthNZDfAP4D8J+LHnsR+KqU8iUhxIuP//3P\nqi301It4pUElPp+PVKp+F2Mpdop4sQjWMy9b13Wy2ayXW61qiadSKYaHh4lGo9y6dctR2VxDY+Lz\nD8DFbG4Zj5e1wqUQjtqvyuZ2V4NO3CA1Hc125iYXloHu17DPP489PlJ1RrnUdLRk9f7r1bD8EeTU\n2O79tHYSPPkcenIFdpwD8yKI/chdLNrWdFKj3owb1WMxjElvDgOlEMEQrFaokc+miWqCwF96N8t/\n9k2QsmJZWT1IKfdlRvyBRTQ29FUvUsqvCSFO7Hj4Y8AHHv//zwAv86yLeLVua42ILxevXbCYE4kE\nIyMjNDU1ORbBcuzl2FDbtnnw4AFLS0sMDQ3R2tpa95r17lFKCVPOy8os35Nxo1L3QUcvSeGnuasL\nIUCYORAaUg+AkUeurcDS7O4a7WgzIu99bTgA/ScRhvNDiUCiZ+Nox09g2zr2+DtlDyKiZwCxUf/h\nw7QEFEfDQ2GC5y6iZzYQZRL9cqvu53En9BZkqvJ0N6cETxzHHPPGLV+K6IXz1RvXSIl/dZq+v/wu\n1qZXiVy51rD9wN7OiD/ICCHQAwfXnV6GHill4VQ4D5sFJNV46kW8IOCl3tw+n8/z6V0FdF0nnU4z\nOjrK+vo6Q0NDxGLley47pREx8VKvzerqKqOjo/T19XH79m3Xrr2GWeIrM+Cwm5nt8yOb2hGXbiOw\nEfksAkkMwCj2i1tPysZaW5BtrRAII00bmViHxHrDrHAATdcoPdy6MsI00DHQzl3GisehRB20MOsP\nF9maD3v24eY/NA3/ucv4ySNS5S18S/gxJ94q+/NSSAT23O7YvdQ0RFcnekcbwVgTMpMj92ASO14+\n/CBCIawGZqQjNPRsvGKS3zYWp+n54R9v2Hb2cj78YUHs4XTJEnQKIV4v+vevSil/1enFUkophHD0\n9nqqRVzTtIri0yhLXErJxsYGs7OznDlzhrNnz3pauua1JV5MoVNcPp+veT45NFDEJ6s3/7CBdMdx\nRDhKeHXadUKbkDbkUpvXRYLYfRchm0WOfx9R6/CMMsieYxUT2pwgcil8QR37/PNYj6YQ65uJZLKz\nDy1Vf7MY0xcFI4/vubMEmsKITPUWt9mk4Tq73Go7QtBeI3D2OfxNYXw+gTAyiFQcbAuQIBMQAnm+\nj2zgNDlbx1xPk5+YRBaFxsKDg5jjjbPCw0PnkHEXB7tIE/7Ldxw9tZbPTS6XU/HwYvY/sW1ZSnnD\n5TULQog+KeWcEKIPcJSN+lSLeDUaYYknk0lGRkbQNI3u7m4GBgY8Xb8R7nTYPHjMzMwwOTlZslOc\nWxqR2KYnV2C98vvaaD9KrqkNTVqY6yv1Z6T7A5BJIKSNPHMJmUohppx35qqGiEQh497tXAotG0d0\ntGH3HcMeH0YLBOpOxLMRSNMkfO3mZmzdgYDbaOTHnbdkpamZ6OWrmPOPiKKBvQ7xyocPAYTzKcIA\nTSAvHSUbjJIxBMZ6CsODngCVCAR151Y44L/xfoTDMFotjV6SyeRWa2bFZmLbQY6Jl+H/Az4BvPT4\nf7/k5KJnWsS9tMQty2J8fJyVlZWtWdnT0/VNTCpFI7wHyWSSdDpNPB53Ve5WiUbExMOLuxOrCphN\nbRhdx5CmgSY3O+81WfWnkstIDJHedN8LMw9BP/LCLZh9iKhyoKi6dnvvtnIsLxBSoufiiMELSN2P\njLVv9gxfW9z0MDjZV7gJWrshEgVbEno0jnCRHJfNa5B3kHwZjsCZs8T8FqZlgIOxpOUQSMK5JGFA\nnj2OzLSxNrOKPeF9q9XA8RPIJRfZ/roP/60POH66ZVmuP4ON6pt+aBGg+Q5udroQ4rNsJrF1CiFm\ngH/Jpnh/XgjxU8Ak8CNO1nrmRbxeS1xKyeLiImNjYxw9epQ7d+4ghCCZTDbEVe+lJW5ZFg8ePGB5\neZlQKMT58+c9WRe89xgEjTTBxNKux2UgTL7vDJZtbpsT7c9n6rfCfYGSlqfIp5HdPcjeYzD+luu5\n31vrtLZD2ps52bsIhtFSj0urmiLI5uc24/xokMtirS2hJ1bBH4C2HmhqAZ8PYeXRCr+PkUKmN/MI\nnGIjyD+o0oQnECJy9Xn8dmYzZm+BlfCqDEzgM3OQSdDd4cc6/QFWX38Ta827MrNwd8dmcxeH+C7d\nRGtyXkpay/TDZDLpWcvVpwGx/+70ikgpP17mRx9yu9ZTLeLV3MH19khPp9OMjIzg9/u5cePGtphU\no+LtXq27srLC3bt36e/v5/bt27zyyise7O4JXjZ7yWazhBZ2C4N5ZJC8Lwj29oOYQHjSlCUp/DTJ\n0jFwISVYWeSp89iZLNqkC/cxYERiBBok4NIf3HU42BbnB7S2Vuy2NgRy8zEzsyu5TuohtIS7+vK8\n5Ucmy3gX/AHCV64REAYi/8RdnvdFkEvehChE/zFYeVL2pa89ouvcUbL6EOvffKXuLnC+ri7kvLuE\nOf+dyi1Wd1JLy1Uv+6Y/LexzYtue8VSLeKOwLIuJiQmWlpY4e/ZsyY5vB1XEc7kcd+/exbKsXYlr\nXma4ehETL8TpFx+Occ1+krQkNR/54xexzPzjhKft+A131mPJe+t+osKi2jLCMhABfdPFPv42IuvM\nhW+3dSEs52VlbrCb2tEqZI4X0Kr9cg5/l637SsiWarEqBKGrNwgGZMmGNmYi5Vn8WrNKeNaMHCEj\nR88HbhOfXiFzv/Y69MiJ46Wbu5RBP3kOvbf0zPBy1CLiyp2+AyHQfErEFSVYWlri3r17HDlypGLp\nVaNEvFY3dUEQp6amOH36ND0920sQC5azVyJeryWeSqV45513aG5u5mpHAPHYuLIjMXI9Jzd7p5dA\nAFoJt7tbZFPrVizcCSKfRp48h1ycQ6xUaAACmMEIIcvbhj0FpKYjcvXXs0s9gFh46OoagyByR4tV\nrbWd6MXz6MlVKBF1SNs6YtHdfcoheo5WTHwU8RViMUH0w+9n7bU3NsvyXGCHQtiL07iRBv8L7qxw\n2NvhJ08zhzCxrSaeahF3KkhOxCuTyWxlnV+/fp1QKFTx+Y3KIq8lYSyRSDA8PEwsFqs64tSLMayF\nfdYzGW1xcXGztj4cgG9slltmWvuQsU6oMATEb+YddWCrhNR9kHVf9iXMPFZbB3lfiHCFEalWZz+B\nRlnhLZ1oaQ9mkJuWa+s4O7vd9R44d5Fwc6BiUlw2maG2IsbdaLqT967Etz5H16WTpDIaie++4Xj9\nlgsX0FwcbERHD/qZi46fX6BWd7rKTn+CEKD7D25im5c81SIO1UWvIF7lPjTF4zbPnj1LR0eH4/s2\nAjfrFjLmV1dXOX/+fMWTuteHjlos8Y2NDYaHh+nu7t7ycsj730ZKm2TPabRAYHcntZ33jXtghUfb\ndk0Tc4ouINwSJR26QHjynV1CKAMhgnZj+vVLqHnK2bZ1hI5YquxN2EmeEPb8405rPh/RW3fwp1fB\nKO9xsPxhQmvedGcTnb2wMu/8glyGqCbwf/B9rL78F9VH2vr8aAl3eRa5C7fQc7mqB/6d1OpOb8Qg\np0OLEMoSf1Yo1IqX+tAsLy9z7969suM2DzIFt//Ro0e5ffu2oyQ/r+u6na5nmubWUJhLly5tJehI\nI4dcnCL33DV0BxngfstwXEZVDqnpnozsjAQE8sIt5I44eaKpk9Y691gO2dxZdYiKM3SE7a5qI7u4\nKXB6dy/R08+hpavH5M2cXXfuQgEtFIGE2x7xkkBinu4Pv4fFv/g2ZMp7R6IXL8Cy85JRGYqwMTDI\n9N275HI5wuEwLS0ttLS00NzcXLGErFZ3+vHjx11d8zQjDniJmZc88yJeKnadzWYZHR1FSllX17L9\noLB3wJHbv0AjLHEn6y0vL3P37l0GBgZ2dbazl2fI9Z5COizh0j0Ytymb2mu2wneyGScfQi4+QqzM\nIXUfsYi/YjigLjywPCQCserCogVMEcCaekDoyvMEfRbCgTvf9gWxJzwaTtLaCUuzNV+urc3TcX2I\n9fF5rLkS2fhC4DPTro4bgZvv5+SZQWAzXJfJZIjH4ywtLTE+Po6Ukubm5i1hj0ajW+99y7IIBAKu\nfgeVnb4ToUT8aaGaO724a5tt20xOTjI3N8eZM2fo6uraq23WjZSS6elppqenGRwcdL33hk4dK0E+\nn2d0dBTTNEseNqRtkU1tlMw+L8VmLNwLK9zbWaPCzCE7urCbYggpGzZExY7Edo0BrQk9iHDSqKWI\nbDJH07vfgy+1e5JZOQxLr7vcq4De3Fp31zt/NknH8TbSvd0k3/jetp+Fzw0h3fTO1334b31w659C\nCCKRCJFIhN7eXmBTqJPJJPF4nMnJSVKpFH6/n5aWFtLptGsRTyaTKju9mMPZsa0mnnoRr0bBEi8M\n/CjEY926s0pRcCk3wg1fnIxXSFxrbW2tuePaXlnixSNZK7V3NdYXHQs4CHQvYuEeWuHFCGkjg37M\nWB9ierh6aVcNyEAIYdaX8S6lRKyXnkhWDrOpnYgvhUg5v87WA9iTzuehV6Q5BkvexNU106BJNwl8\n4L2s/vlfwONDaCCkI11EKXyXb6M1Vx52pOs6sVhs21CkfD5PPB5nbW2NmZkZpqeniUQi29zw5b6X\nlIjvRCA8+A4/DDzzIg5w//59dF3n6tWrRCIRz9YtHBC8FvGClVtIXFtfX+f8+fN1fYj3whLPZDIM\nDw8TDAYrjmSVtoWx5tylG7QOphVejBXrxZQS6/hlArMj+Dx0qZu+IJoHjWOkL4yWdp7QZp64gEgn\nXE94M6QPStVz14DW1g0LVcaBukISSC7Q9eH3svKN1/H39LprsYog8K6P1HTnQCBAZ2cny8vL9Pf3\n09zcvNUOeWFhgbGxzbbDxW74SCSCEIJUKqVEvIhD2ju9Jp56ES+X0GXbNlNTU8zPz3PkyBHOnj3r\n+b0LIl7P/PBy6y4sLPDgwQMGBgYYHBysOxve64ElxdnpUkqmpqaYnZ11lOFvri85/pIXQiAOWCx8\nJzZgan6wDKRlkO49Q2D1EaG0N61Ac74wEbv+kjWRcuaStgNh7JPnkfkMmksBtXU/9pRHsfBoC8Ij\nK3wn+to8XbcukZd+rHHn7wt98CJaV29d9y4ktgkhiEajRKNR+vr6tn6WSCSIx+NMTEzw8ssv84Uv\nfAGAb33rW8RiMbq7u2u67y/90i/xa7/2awghuHTpEr/+67/uOrP+wCCenZj44Um39pC1tTVeffVV\nDMPg5MmTDauvbETDl2w2SzKZZG5ujhs3bnDs2DFPytm8nlNeOBQkEglee+01stkst2/frirg0rZd\nWeGBAxoLL8aK9YL1pH2rjsRs7yPfe6rutaU/SFjWX7Im9RDaRvUSKqvjCNaJs2Bk0DJphEuL2iCw\nrcd9PWidPS5CLu4RPh/RmJ/A0CXH19RqhRdTaQCKruu0trZy7NgxLl68yD/6R/+I3/iN30BKyVtv\nvcXHP/5xrly5wquvvurqnrOzs/zyL/8yr7/+Om+//TaWZfG5z32u7t9lPxGatm//7SVPvSVeTGFW\ndi6X4/Lly0SjUWZmZjwfR1rASxEvWLMzMzNEIhHOnTvn6fxgXdc9nToGT7quVatRL8bcWEJazr7k\nhRBoXljhze2uurO5wQYs327hEoDhC2Ifu0Rg+h20Gg8isqkd4aDFalWqtFi1Afu5i0gkwswjJWjz\nNVjh0x5Z4eEmRB0Z6U7Qu3oQGwuE/eC7827Sr36rYj25duQE+onBuu/rNgR3/PhxLMvipZde2vrO\nqcWrZpommUwGv99POp2mv7/f9RoHhc0Ss2fDRn3qf8tCbHZqaopvf/vbdHV1cf369S3r2+fzNaQ9\nKngn4hsbG7z66qvkcjnu3LlDOBz2vBuclzHxtbU1Xn99s8varVu3HAv4phXuPCYbMPPVm3RUu6em\nQ67+uvBy2C3dyAqWp2VbZI9fwg669wZJzQfZ+uvCs6asWFZmByPYZ6/zeLo4ACKXdd1YxiAIhje5\nAFp3n2dx9ZI0xxBFyZL+9ArNL7yA1lQ+Yc0LKxxqqxOHJwOddF13HcI7cuQIP//zP8+xY8fo6+sj\nFovxkY948/vsD5uJbfv1317y1It4PB7n1VdfJZPJcPv2bXp7e7e5n70YR1qOekXcNE1GRkYYHR3l\nwoULDA4Oout6Q9z0Xoi4aZoMDw8zNjbGlStXCAQCriwKM75cUfCK2bTCdydU2ZoPs7mLXNcJ8rFe\nbK2ys0k2t7t2CbvB9FfvMSBNg0zPcxit7mKpdqwT4dBrUYmA0Mq2WDXa+7COnQHjScy9Jitc82HP\neGSFhyKIZXfT1dyi9w7sCtNoyRWahk7jO35y1/NFWyf60DVP7i2ldPW58cKDtra2xpe+9CUmJiZ4\n9OgRqVSK3/qt36p73X1DKHf6U4OmaVy8eLFsI4SDaokXslGPHz/OuXPnth08GtGXvd41FxcXuX//\nPsePH2doaMh1nF5KG2PVnRVuB6JY0VbsYART6NhyM7N9i1AAQi1oug9NWvhySfTECvrjVqBS8zXU\nCjebOssOatmFbZFv6sBqaicwd6/0NK4ipNAQHsTxpeZDK5EcZvsCZPpPE/Cx+6CQzbquJTdFCPLe\ntJvVeo6Ay0OEK8IRRLJ0yZzIpYi0hcm33ST7vW9vPe5/4cP7PvqyntyYP/3TP+XkyZNb/SV+6Id+\niG9+85v8+I//uFfb21uEQDwjiW1PvYg3NzdjGOWtleJmL15Ti4gXBq34fL5dM8rrWbcatYp4Lpdj\nZGRzlna5/TrBjK84Ejxb82FEezBz68jgYze9DZW6jNiWuZkh7o9CexTTsvFrgoA0Caw3Lq5qBqMu\nu7NJLCBzZAh/LoVv4UFZV5ls6fQmm94WiKK/uy007ONDSJ9OsETrVSlt7EfOR3HC5t/MmqlwTVMM\n0dSMXJyrnqgWDFWdElcv+pGTiHiFaWi2TZAE+rveQ+rbr4HPj//quxu6p0oYhlFTb4hijh07xiuv\nvEI6nSYcDvPVr36VGzdueLTD/UGVmD0jNGpkqNu1i7vFVSvDapQl7uYwI6Xk0aNHPHz4kDNnztRc\n1lJYq5oVbgNrWitWuIN2mUDW8fv7dA0LQcrfRLZ3iMjGI3wel5dZ0XbnVvhObAvDH8I8foXA+hy+\nHcl7EsCu341uo6EVuaWt/lPYTS0IM1e2d7owbAKWu9/L1MIgbUTPEbSWVrRwBM232Z/dziTxbZ7C\nkO1nkaFmLMPEWl7Cnp/earhSQOsZ8LgufAf+gOPDkS+5TPON58nHBhAuO6x5SSKRqLvl6u3bt/nh\nH/5hnn/+eXw+H9euXeOnf/qnPdrh3iOEavbyzNBoS7ySF6BAYXpXZ2eno25x+22Jp9Np3nnnHaLR\naM0d4oox48sV+6PnI11s0IQlBUEspAfJXLYvCNLerLtt6iHQ3EN4+QGay8Ef5TBCLWDW5z6WlkGu\nuROjtZfg/DjaY9e/bOlEePAaWBboloHV0Y/s7AMjg6iwZykl+qLzISCWppPsGCCSiRN+7sTjuLsB\nuY2t2eLFngZhmYjUGhrgbwkh2y9gB6PYeQNzcQG5voxYc9dYxi3asdMIF/PoRTaJ/wPeWeG1xLe9\n6tb2yU9+kk9+8pN1r3NQ2O/wxl7x1It4tThRoy3xbLZ87NAwDO7fv08ymdw2vasa+xUTL/YWDA0N\n0dbWVvd9K8XCzWALyUAXWfPJF1szybqblppSIqW9LZkrL8HoOk0onyK05lyoSrFphXs3btS2TDLd\nJ/FJC//sPW/WlCDyOcyz15FGBmFUbxYjTBuRrt4QRvr8yGPnEEISzRv4E7U1ohFmHt3MowP+tijW\nmXPY8Q3se29BA1rXouloLifYyeMXIejdgKRaJ5ip4Sc7UJb4s0MjBLFAuQOClJKFhQXGx8c5ceKE\n60SwRhw8hBAV14zH4wwPD9PR0eHpWFZzY2WXFW77QiQjfaQNAUUCLow0kvoT0fJSp5TzU9o2GV+Y\nfO8QkfgcPgfTuEphhJq9n1QmbUwE5smrIEHPJfGlVtFdDP6whYbd1IEZiZFOJmhpym9a305uLyV6\nle5oUvMhj58DDYSVR6Lhc9G4p+LaPj9aeh2dPPaVG5iPZl22Q62OOH7aVc29FBpy8Lqne1Ai7h0q\nse0ZwYtuZ+UoJbbpdJqRkRECgQA3b950Pa0INg8eTtz0btB1veRhptCffW1tjQsXLnjan3nTCt/+\nRZyPdLJOS8mQb8SKQ72fS92Hv0rCi2VZJKLdBJq7CS9PoLko46orFu5kfS2AbeYxAk0QaIJ2DV0T\naJaBL5tATyyjGxlsIbCj7ZiRNqxAeFPAC+9FKQmz5mqWt7AkIln6UCM1HXnsHPi0zdrxwlte4rqW\nvByytQftcd22lonjb2/B7juKOfqmJ1nvEvBJd6EUOXAWIs56IDilVhFXfdO3I4Ro6Hf7QeKpF/H9\n/EMWi3ixK/rcuXO0t7fXtW4lN30tFPc6L1CY7HbkyBFu3brl+WtpbixvCZ4E0s3HSJil35JhYRDS\n63ehSn8I4bDhSN4Gs/M00bjzxLeGWOGPkf4w9s61pY1lgYWGEYpBKIbQ9MeJf49fL1tSnL0fEJKA\n05mhFGLhu61wKbRN8fbrm2JtFv9MbEuaqwdTaJBY2R4/lxI9u4F25hxm1sAeH67rHun2PlodhAoK\nSEAOep+9rSxx71CW+FNEtdnWjaIg4mtra1tjTr1wRTc6Jm4YxlZ72mvXrhEOexfzKyDtJ7FwWw8Q\njw6QNcr/jSJ2/YlcUvNhuewYZtsWieZeIsEmglXK0Rpthdu+gKOOZ7JSmZaU+LPuBq9sWuHbr5FN\nbcj+E5u16ubu+wlbeGaFax39W1b4rvsYWfw62FdvYUxOwJr7kbQSQTDocrJa73PQ0un6XtVQlrhH\nbI4x2+9d7AnPhIhXo1Fzv6WUrK+vk8/nt3q1e0Ejs9Pn5+cZHx/n5MmT9PX11W19F889L8bcWEKa\necxQjDW9E6uCgDf5TMjU7zJN5k3CwRpKgaQk7Y9idZ0mtDRWtna7oVa4L4jtQctSv5CIvLtEM21H\nj3J7YBD8vrLNZqTQ0Ja9qb+XvgAiVT03QUtv4O/qIN3Zg298eFvtezXEkROEjaSrfdlnb7p6vlOU\niHvHQU9sE0L8LPD32HTsvAX8XSmlaxfrs3FUqYLXoiilZG5ujjfffBNd17lx44ank9IaYYkbhsHK\nygqLi4vcvHmT/v7+ugW8lIsenljh2aYjLIsOLLuCl0RKQqZzN2dZ9EBtAl5EDo1U7xC2vrsvdcOt\ncAftW50QyLqshzdtRGIz2Uv6A9iDzyN0gahg7QsbhEeTymRrt+PWshqSJmEgBy9hBJy/Xprf3Ze9\n7DwCHY0ZDnLYRXw/PJ4lEYAm9u+/atsT4gjwPwE3pJQX2cz2+e9r+VWfCUu8mju9UCvuxdzvdDrN\n8BPaC50AACAASURBVPAwoVCIGzdu8L3vfc/zWLLX09FmZmZ4+PAhoVCIy5cve7IulPdw5OMrxKMD\npBx8N7f4TaQHVrj0O3NFV8O0LBIl4uSNtcID2BXq6J3ix0a4bDOrLW+GPGRHH7K9G1GlBEuioS17\nM+Nb+oOOrPCdhO0scvAs+aVlWKi8F9F/Et3lBDt7sDFWOBx+ES981y0uLhKPxwkEArS0tNDa2rrX\nOznwljib+hsWQhhABKgpieSZEPFqeNHwxbZtJiYmWFhY2KqhllI2pHzNK0u8MCq0ubmZ69evMzxc\nX3LQTkrt07YlixkfedPB/qUkkN+ovyLYH3QdC69EIU4eDUYJrD9quBUu/RHwQMQDOZd5BZaE+DL2\nc5dAGgijuqdP2NKzgTKytQttw32MG0DkMwTaWjBjlx7XlZcmJy1XX4Iy1gW9uwegeEUtIp5KpQ6E\niK+srPDyyy8zNTXFxsYGq6urWJZFT08PL7zwAs8//zydnZ1C7oW5LgQcYBGXUs4KIf41MAVkgD+W\nUv5xLWspEad+y3ZtbY2RkRF6enq2Ja41KjO+3v0WDhyLi4sMDQ3R2tqKaZqeHzhKeUA2kllnAg40\naxlk3oP2oprPkzal25CSpC+K3nacgABctiJ1fBvdj+WBgPuEdN3lTcTXkGefd2y9S6GhrXhohSfd\nJeDtRNgWfiysy7cw334ddry/Re8AUctdfkAjMtKLsSzLtUfwoGSnf+1rX+PP//zPiUajDA4O8q53\nvQvLsnj48CG/8iu/wsbGBsAPAH+wF/vZ545tnUKI14v+/atSyl8t/EMI0QZ8DDgJrAP/RQjx41JK\n16PjngkRryamtVri+Xyee/fukc1muXr1KpFIpNYtuqIeS7zQ4rW7u5vbt29vHTg0TWtIslyxiFu2\nzbrT7l22hWasO4ovVSQQwvYoPrsTIQRpLcKS5afbXsLfgO8MGYh4EgYI5FwmbgWa0FssV+53Ydne\nWeGxbrQKQ0jcoGc3EJdvYNwbhvST10FraoK48zwiI9REpu0IkTLJml5wmN3pp0+f5qMf/WjJQ8jP\n/MzPsLq6SkdHR04I0S6ldN5Vpxb23xJfllJWOvF9GJiQUi4BCCG+CLwLUCJeC24t20Li2sTEBM89\n99yuGeWNphZL3DRNxsbGiMfjJVu8NqIMrxATL7CRyGJXSmIrImzF8dUp4JLNGO3jMWcNwQ62oVuw\noTXRkp0nYNfWYrQUmyVx9R9AdAGawzp3G0Gm8xTRtSlXs8ql0NGWp2rd4va1AiFE0tvveC29QeC5\nMxiLi8jFWUT3EbT4sqs11nvPMjvxkEwmQzAYpKWlhVgsRktLS93zAwrUKuItLd42namFS5cuAfDp\nT3+atrY23vve926NNpVS0t7ejpTyT/ZiLwIQB7vEbAq4I4SIsOlO/xDweuVLSqNEHHeWeCqVYnh4\nmEgkwq1btzxJhnOLW0t8eXmZu3fvMjAwwNmzZ0seOBpxCCnep2U5t8J1LCIiX3d7bBGMYDVouA2A\n5YuSf3yWMm1YC/YSI0Eo404cyiGDUU+s8GDemRVuBqIkYwMEjBSai3auAMIwKmasu0G2dJatC68H\nkU/jb49htrRudqtzcQ8Zbqb96rtp1zYFNpvNEo/HWVlZYWJiAtu2aWpqIhaLEYvFiEQiNX2mDrMl\nXtj75OQkX/7yl3nzzTd573vfy5UrV7bEfM/Yf0u8IlLKV4UQvwN8l802SW8Av1r5qtI8EyLuxRAU\n27Z58OABS0tLW3Fkp/f2uga9XOnWTvL5PKOjo5imyfXr1wmFQp7twQnF1v1aPLNzqmRZWn1ZMOqz\nniXCsdVfK1mxvYxJSlinmaZoiGhqxlFP8nJITcfyIAygAcJBD/hcrJ+Uvxlp20Ti7vqdS82HtuJu\nxnjZtYIRRGLFk7VKIWwLPdaBDDchEysI6ex9JgdvgPZEFEKhEKFQaGsEr23bJBIJ4vE4ExMTpNPp\nrczsgrXu5MBfi4hnMpk9C+VVQtd1pJR86lOfIplM8rnPfY5PfepTxGIxPvGJT/DBD36w4ohlzzng\nbVellP8S+Jf1rvNMiHg1fD4fmUx5K3FlZYW7d+/S19e3LY7shMIBwetGMpUodvefOnWKnp6efWk/\nW7DETdMinnQWewxqFlSwAiU4EkcRiiA97i9fjO1vwihz7ktafozoCWKZmZpHm+a1IJoH4Y2Qmar4\netlCJ915ipzNZk91M43mNgEum0V4FIqRze0NscK33aOpFZFNIM9eQ07eRWQqeypkKIo8cbHiczRN\n27LCBwYGAMjlcltZ2g8f/v/svXuMZedZ7vn71n3f617V3dU3t+2+OE4cu+1OHBhFQkgJHAYJIyER\nhIbBBPHHISgahiEwEiIRCVEChIB0dHQUiAIS4iAGUEAczeQoJMrFsZPYjqu63ffq7urqqq7Lvq+9\nbt83f+yu6rrs+167u9pVj1SSXb3rW2vvvdZ6vvd9n/d5r2+J1rPZLKlUasd92QuJK6Ue6POlFdbf\nT7Va5cUXX+TIkSN84hOf4Dd/8zeZnp7m1Vdf/VngXwauUBcC9L1Bb3vjXbZBs0h8PZINgqBn+9H1\ntR9U2t11XWZnZ7Ft+6Gl+9exHomvFt2OM+MZqvdq2SDNJFJPEOkWgdKp1AI03cQyBLaIMKSL4ZcQ\n24hSCQ3ZwAo0LijApXVWw4sEK85hhoO7GF26gUVo9bC+z32XBohKc4V36GQpZw4SrZdmlCJZ6iEK\nX42pFp7IIErxlCKaQWZGN1T6wqugph/DW7qDXWguolNPPNcTIdi2zcTExJZovVwuUygUuH79OtVq\nFdM0N8g/m812TeK7xlxlE/78z/+c27dv88YbbzAxMcGf/umf8uM//uPMz88zPT39ReD/BRrb/cWJ\nfkWxjwj2BIl3q05XSjE/P8/c3Fzfkewg55VvhlKKGzduMD8/z8mTJx9s2qoJNE0jCCNKbvv3rxSY\npklZDBEkhglCVSf+iI3ZHdo9pzQ/VPhoQAr0FKYlsESIKT2MoIRm2agY+8K3Q1oZgg4C7EjCij7O\nkJHAdjuPLkUigxbD+beKwu8aw2ip8S1tV8nIRat1t+EQ1daRfjdQqWzXYrOuj3EvCl+HCH2skVG8\n9BB2g1ntynJQx+MxQNI0jWw2Szab3RKtF4tF1tbWmJubo1gscunSpQ1ibxStb8dum9j1+uuv8+EP\nf5jPfOYzG7+TUnLo0CGAzyulBk/gsKX88U7GniDxdthMtOVymdnZWdLpNOfOnetbdfogSLxUKjE7\nO8vQ0BDnzp3rOh03KAghcDvgIqXZFPwUI2b5notbd9FFECkCdCCJZqTQEKT0PHoU76S39TNzpd3V\n69dUGiedIl1bxAhbi/tiq4UL1TAKD6001dwhtO16AaVIdF0LN9HzjaNwCZDMgNDQKu2V8SqZQxQH\nVwuHrVH4ZggUtqWhTj4HV97cYhmrHn8WjMFls2zbZnx8fEP49b3vfY/p6WkKhQJzc3NUKpWNaH29\nvr45uxaG4a5Jpa/jS1/60sZ/r+uB1s9RKfWFB3ISu1zYFif2SZx6JB4EAZcuXWJ5eZkzZ86Qy+Vi\nWXuQJB5FEVevXmVlZYUzZ87E0mbSbGBJL9B0kyBqXsVWwqQSpSlUNMbTPkEMKXBN13F9cBkhYwY4\nwQpajC1m0srSi+C9FgpqxhRpO8CpzGM02agoOx2LIj0qLG/51CPDxh0+gifFvdGkW5GKqmhd9pKL\ncgHppFCpHDgpMC2UpoGSEPoborFw/CAIA1GrIlbvoDXoPVeJFFop/k3XlmNsi8K3Q/gV1Il3oW7P\nIUqrKNNGnXhmoOe04xyE2IjW17EerefzeW7cuEEYhqTTaS5dukQmk4nF6CWfz/Pyyy/z1ltvIYTg\nS1/6Eu9///t7WmtdAySEeLgbjN3dYhYb9gSJtyOlQqHAysoKw8PDXQvX2mFQJB5FEa+88goHDhzg\nhRdeiOWc12vYsZG4maIxgWu4ZFgt64BACIWl1ej3Y9K1rZF/KTCpalNk9QpW0OXgjwZQQFX2N0Sl\nHJmU7SMkowKZML/l04lTkZ5QdZe3CMFdaxQ9NYQmm3yvSuF0EYVHiSxRchjDWtzUViYhrDX8tusj\nSX3QQY5PIU0HgcBbvYtdXq2XDwaoSIfmUfiOc/Vd1MRBVGYYlRkFs/Osy6CwPVqXUlKpVPj2t7/N\nl7/8ZWZmZviJn/gJ3ve+9/Hiiy/y0z/9010f42Mf+xgf+tCH+Id/+Ad836da7T3jvSsygfuR+N6A\n53kbLVipVIpjx47Ffoy4STwMQy5evIjneTz//POxZQzgvpo8jg1Bqewitk37UkAoMqxUTCJ1/3F/\nIOMRRf1Hy4qdN20kYU2mcIwkGbmGJnuP9iIr19XI6aYQGlVjmNAeJhOsYPp1NX5cUbgd1sWBteEj\nuHoCs434yfHLDaPj7YicLF5uiigMSNXWeuoLFwD3PNjtTBqVSSNTo3D3JlrMBi+b0S4K33KOMkQl\nEnVB2y6EpmlkMhlefvllPvCBD/D5z3+ev/iLv+C73/0uFy9e7JrEC4UC3/jGN/jrv/5rACzLwrL6\n26yuY731Lp1OP3hy34/E37lYn9x148YNHn/8cSYmJvjOd74zkGPFSeJLS0tcunSJo0ePUq1Wse14\nowRd12PxT19cXGKtHGBa9xXcSrNZrqbwo62xmqlLkDF4g+sabosgthYKaoyQsQIcbxlNdFd3V0JQ\nlfHWRv0IVrRRkulhUrWlWOxhNSDUbdzxU3XVeRsCV1Jird5s+ZrIyeDlDhBFIUQhluh+GlozhFYK\n3a8QDY0SjUyh37rYc1teM3QahW+GGjsC1oP1VehFaV6pVEin04yPj/MzP/MzPR332rVrjI+P8yu/\n8iu88cYbPPfcc3zhC1/oeXzy5mze0tISX/ziF3n3u9/Nz/7szz44r4o9FInvia3K5vRwqVTie9/7\nHpVKhXPnzg28hzoOEvc8j9dff53bt29z9uxZpqenYyPczeh3Oprv+7z55pssraxtIfBQy7BQ2kng\nAJPpGrLPNhmlIJSdXcol32SZCVzV3QYoNIe2z8+IDdVQY82ZZtWcpmxP4VnDSK2zDYMCQj1JzRql\nZB/Ad4Ypm5n7bWNtkIkq2DQmTVdYrGYPU0mP1wn83gHNcjypbwmg3YsjlILIJ5p+kmj8SCzrr0Ol\nuxuDqTQdNTm4SWXN0EuP+HqU2w/CMOQHP/gBv/Ebv8EPf/hDUqnUFmV5t9hst2wYBseOHePrX/86\nn/zkJ9f/feBSekV94/2wfh4k9kwkHkURly9fZm1tjdOnT8eahm4FXdcJejQdUUpx+/Ztrl+/zhNP\nPLHRb7q+7iAGlvRK4ouLi1y+fJnHHjuBr2zCSCIl5P0kbtQ4NZeyIsIYRng6lknZ63wjoIROUY2g\nmR520D6Fq4RONRrcrl4A1UBDKahhARaQQTfA1iUWPqZ00cMqUrcJtQSBsPGVjh+KerAd1o1yLLrI\naiiJk985wjiy0/hDBwijiO1bibBaQIT9Z04AXM0hEW1bK/KRloU89jT64nU0t8vxqdvQcxRuxJNO\n7gYPy3J1enqa6elpzp07B8DP//zP90ziN2/epFAo8K531c1xxsbG+LVf+zWCINhQ1T+QUaSI+xvE\ndzj2xLtUSvH973+fyclJzp0798CHldRq3ddhq9UqMzMzpFKphq1ucc0U73dN3/eZnZ1FCMHzzz9P\n1Yuo5qsozeRuNUGomkeUIwm3o37rdnCDHp4JQpAPHFLmJKlgsWWvc2DlUIMzf0MzLFSDvUwkoSo1\nqjiAA2K4Hr42+Yoyhovq4vPMBKUdhOyNTOPrNs1UhtkonhZfiUDXBE3bCQOXaPQAkkNo8xfROrRH\n3Q6VziG66H2vR+GP9XSsfvGwSHxqaorDhw/z9ttvc/LkSb72ta9x5syZrtZYT6FfuXKFv/zLv+QT\nn/gE733ve7lx4wZ//ud/jmEYfOYzn0EIoSulBm+cIQRqv0/8nYN1gmlH3nEqs9fRbcQspWRubo6F\nhQVOnz7N8PBw03UfJokrpbhz5w5Xr17dyBJIKVm7WybSUiyVbaRq/lkOJwOCGIaTWKZJpYsofDsq\ngU6oHyArl9EaMLXSDNxgcFUnIUTLWn6ncPQIFXa+WVRhgL0pCpe6SW3seD1t3iRQcqQfX706PYLV\nrq6uJApJdOQ0qriKvrbQ1SFkbqIrAoeHF4VD7yQeR4vZF7/4RT7ykY/g+z6PPfYYf/VXf9XV368/\nN9///vdz4cIFPvWpT/H000/zxhtvcOTIEX7/938fgAdC4PdP6oEd6mFiT5A4tB8ask62cY0U3L5u\nJygWi8zOzjI6Osr73ve+lirxQc3/7oTEPc9jdnYWwzC2WLuuFWtUoiyr1XafoSJluPTbFq5rgqrf\nf2bOiwSr2jhDWgEj2kosvjngKFw3ieOxltarXUXh2trtjVGjYWaMWmIY1UJ6r6HQS/F4mktNh27K\nKKGHTKZQqZMYt97u+M9UIo3oovddaTpq4sHXwtfRK4nHMSHsmWee4bXXepqEuQW2bXP27Fn+4z/+\ngz/8wz/k4x//OJ/73Of6Xrd7CNS+sO2dhW6tV+NCJyQeRRFvv/0258+f56mnnuKJJ55o2+Y1iHT6\n9vnf27FuR/vaa68xPT3N008/vUHgXqC4tprogMBhKuMTxtBSpulmx5PR2iGSsBLl8MyRjd8pzcYN\nBreb79TRrh3qUXjndWpNSoaDIhJBbfwxXDuLatMuZoe1jid+tUNJGtDFrPJ1KBURHHu6I9GfHJ7q\nisDhXhT+EPvCeyHxSqWyK8aQrj87//Ef/5Hf+Z3f4YMf/CBvvfUWt27d4uWXX2ZlZbA+ADsgqLeY\nPayfB4g9Q+LtMChTlnbrrq6u8sorr+A4Di+88ELHN+SDFrbVajV+8IMfkM/nOXfu3I7d//VlQdVv\nT3imJtHo35nLNHSqXvxy8XzgUDEnUYBnDPbhKHSz35HpQD0K7wYZbxVfM3Enn6ATOYEGaHEp0nWT\ntNVHhBS4RIefRCZbuxMqu7thRQ87CoeHm07vF+sZTKUUf/zHf8yv//qvc+bMGf7u7/4OwzD493//\ndwCEeFAMV6+JP6yfB4k9k05vhwcdiQdBwNtvv43neT1NSHtQ6fTNw2BOnTrVcLBKuQaLHRqiTWZq\nhGH/LWWR0ujWY71TlAMd3zgEYYCI0bJ1M5RUsUThCT3sKgo3VAiajjd8EL1D5xrHLyHi+qyT3QnN\nGiL0iEYPopwM+ur8jn+WIwe77mN/2FE4PDxhWxx49dVXOX78OC+99NKOf/sv/+W/APVoXamY0jkd\nQO2bvbyz0C6d/iAj8Tt37nDlyhWOHz/OgQMHehLTPQhhm+u6zMzMkEwmWw6DudJ8iuMWpGNqKbMt\noy8xWycoeAn8KMV4ooQYQFE8imn2V1p36VRrJtEwdB1PMxt42zWGIRRaNd/z+W05vulATCYxyBCZ\nSKIOPYmxafqYBJRpIfzON+SRAh5yFA6PNolfuXKFf/qnf+LYsWOcPn2aQ4cOYVnWRmB05coVFhcX\n+cVf/MVxpdRgB8ZDXdS2r07fW3gQkXitVuP8+fPous7zzz/fl7Whrut4Xjz9upvXlFKilOLmzZvc\nunWLU6dOMTIy0vRvVkpQ6DCbOxxTS1ltgEIzACEMKn79AbBQzjCeqmHGOP5YSklE/1Ff0giRHUbh\nkebgqQRJr7U72xYohe02n0feNZw09BuFb4FCoahNn8a6famunB+bRvjdfVd3VIKpXeCRHkXRlgll\nnWC3kPgv/MIvUC6XefPNN3nzzTexLAshBMVikbfeeovHHnuM3/3d3+WBEDj3zF72SXxvYVCR+Hra\n++bNm9y4cYMnn3wyFjXpoPrEXdfl1VdfJZvNth1rKhVc7fCWHE3F01JWJ8DBQSlFKbj/QFcIlioJ\nhhMGSVFsNpCtK0RSgNb/QkmtSrvkpFLgG0OseQ5HjO5atCyhYrNXlbET+H3oKqA8fhR7eb5uI9vF\n3yrN4HaYYGogZ9Ydeo3E45he2C++9rWv8fLLL3Pnzp2NACAIAg4dOsQHPvCBh3JOKrZJ97sbe4bE\nH5Y6vVqtUq1WKZfLscwnX0fcJK6UYnV1lXw+zzPPPMPQUHuryoU1OqrrCqFI6JtayhSgGShhEikd\n/54bmmOEaMpHyaBhi2cQ+CjNGWj7p+tFeGpnLW3NNfHMIYasEqKPbYSmaUjRf4SQMgJUm9KERKek\njVL1NHKGixZ0Q8gKsxxj0KSbxDM9pjEShiA48R6oFKDa+SCVaOwI6s5gNhfdohcSr1arPXucx4nf\n/u3f5pvf/Caf/exn+cxnPsPzzz//kM9IoPYd2/YW+rFHbQQpJdeuXWNpaQnHcTh9+nRsa0O8mYNy\nuczMzAyGYXDkyJGOCDyIYG65/dpKKsaykppMEEidWqjhBY13yYV7lqO6pkjZCkcPMYSPjHyEEESR\nQtcHK1bxxVBTvVw10KkFGcaTZQzRGyEpYcQSzSdFtaXkLtSTrAUZwnvjR0dUd+pyW4b3Roj2D5ka\nAt+NZa1mUEIQaiYqNYxI5bDvXmv/N7pBMHIY/e7Ftq99EOiFxJVSu2L053ve8x4++clP8pWvfIXh\n4WGOHj1KMpkkl8uRSCR48cUXH+xsccED9zB/WNgzJN5JJO668TxoCoUCs7OzTExMcO7cOb773e/G\nsu5mxBGJSym5fv06i4uLnDlzBtd1O54jfGMZwjaH15DkKwGabiNV55daJAVFV1Bc9xFXEcNJSaDo\nWJDVC6RwNkiv6WvQWaxkcOQyo9nuzkbXNaox7BMzpo9s0metFNSMEfLe/aTyqFkGv/O2PoHCiCkK\nl0IwsMkxmxBmJlD3NrU+GtHUSZylKy0d5m4FNjff/BFRFHHnzh1yuRyO4zxQW+bN6JbEH4gFeYf4\nvd/7Pf72b/+WVCrFj370I1599VUqlQqu67K2tsYPfvCDrjtw+oFi33Z1zyGOyDYMQy5fvkyxWOTp\np58eaP9mv+dbKpWYmZlhdHSUc+fOoWkanud1tDFwfbjdQrBsaIKKZ7Bc1jiYrrW0X+0MGmVfx/WH\nGdIDHMOnqYF4jxAI8m6Ht4PQqOkTFAOPlF665wHeHlEXG5nmUNhUGyYLpDApMELN23Q+SpGNuovC\nnbDWcFa4FDrSTqGsBCKoobmF9kYTqZH4FOlNoDR9R797FIVUJ06QKNxGbzBERRkWB8+8SNatcfHi\nRTzP49KlS7iuuxFB5nI5MpnMA4sge4nEoX2A8iDwxBNP8Ad/8Ae89NJLPP300w/7dID9FrM9h35r\n4svLy7z99tscPnyYkydPbrmx1p3Q4nwY9NonvjnN/9RTT20RxbRzbFvH1aXG9tq6AD8yuL2moRCM\nZ3ww+q/XZRKwVhEgIF+zMDSTsXSAimqx1ccD5XS92Sj5NlVhMZr0MFSl5blomoYbQ0k4Z/mobdep\nRMPTcxR9G7nte5m0iuB3Hv4LIVBRiJ+dQho2UjOQCJSSqM3Xhp5AJEbRNYEeeRiVVfRtqnCpGRD0\nb+zTDkF6vOHAFhWFVDNTOHYaM79V1KcmHgPdQCmF4zgcPXq0/nulcF2XQqHAwsICFy9eRNO0DVLP\n5XJ9dZW0QrckLqXcFQS+GbuFwEHEoj15FLBnSHxQfeK+73PhwgXCMOS5555rOPR+fe04SbyXPvFi\nscjMzMxGmn/7+XSSol+rwMo2HZBGPc08v6YT3SNCISQpW+JH/b1nU1MU3a3fXSgFd4oWKdska7uo\nPodyCKGTd3u74SMlWKo4OIbFsFNFUztbvqRUuH6E1reoUWHK+1F4XXmeoxA4ROHO61tDkgw7E3lJ\nTcezx3CiMtX1+FrRdJpZ/fiSMIIQAy81gcjo6EJh+FWMygokcwNTpG+cg24RtrpmlaRmJokmTmAt\nXUEDlGGj7s0sl1JuIU4hBMlkkmQyyYEDB4C6MVOxWKRQKGyortPp9Aapp1KpWMi0WxKvVCq7QtS2\nKyEEapeTuBBiCPhvwLuo323/u1LqO92us2dIvB26jcSVUiwsLHDt2jVOnDjB5ORk0xt5ncS77QFt\nhW5IXErJlStXWFlZ4V3velfTvtJ2JK4UXFnc+jtD11hYM/Cjre/92FiEF/a/abFM0dS/vOIJKl6C\n0ZTEFFV6dXBzQ5t+1Wa1UGOhnCbrOKSNMmLTVBPTMglicDgesjxUGKEUhEaGQpgk8Jqf95SVB6/1\nxnSdvCuRQUr5qD4iZyUjQiDUHRg+htB1EmGAFtP88UYI0mMQts80BAqiqZMklq/D1IkNI5BOMmSm\naTI6OrrhViilpFKpUCgUmJubo1KpYFnWBqlns9meulCUUl1t9HeL5epuhOKRELZ9Afh3pdTPCyEs\nINnLIvskfg/dROKu6zI7O4tt21umeMWxdqfoNJ2+LrKbmprihRdeaPmQaLcxuL0G1U2CZakM5pZ3\n7naTliSIJP0SY9JSFKrtHmqClYqOoaUZTXoIulNUC2FQ9uPbsRdrBiWRYyThY4syKPBj2MwIoTCi\nKoGepBhl8FqQN4AlQmy/uVGLLwVRaoJKZNSnnymFI4uxGdkqwyIMA4L0FAkVYhXmY+/alYZD2AGB\nb7w+CnEnTuCMHr7/ux7KXJqmkclkyGQyTE9PA/XJfoVCgZWVFa5evYpSimw2u0HsgxDM7ZN4a+zm\ndLoQIgf8L8D/BqCU8qHLh9c97BkSj6NPXCnFjRs3mJ+f5+TJkw19xBvhQQ8rgXpq7vLly+Tzed79\n7nd3lHZrtWYQ3m8p0zUoVE0KbuOH38HhsKNhKK2glCKMOl8jlILFssNwUscWbmf7BwXFIH6nLqUE\nK1UbU7cYSdSIIkm/QjwjclllhFrQ2S07aaxCgzGtUjNwrREqgY7YtLkYMmooL54+bmHa98lVKVx0\n/JHjJNxVDLdDk/0OEKRGOorCN8NID8Em0o6rzGXbNhMTE0xMTGysWyqVKBQKAxPM7Ra3tt0JWIfO\n9gAAIABJREFUsduFbceBu8BfCSHeA3wf+JhSqmsV6J4h8XZoN2+8VCoxOzvL0NBQWyez7RgUiTc7\n37W1Nc6fP8/Bgwd54YUXOo4AWpH49XstZYaucXvNIGhCsJPZcEu03iuyDqxVu98IrFVNUpZGxmqf\nXleaHUvKvxmiCBZKSYJIYGqKpB1h6xEyrGIaAq3B96IUCE1HKp1A6nihhh8oso4GHeoLUrqH4Re3\nrouglpigEhqoaOu0RF1I9G2v7xWK9Qho64YgiiLKVg7LGSJRmEf0qWOQVoqoSwIXhoW+bfrZ9pp4\nXNB1naGhoQ3PhU4Ec91iPxJvjvp1+FBJfEwIsXlA+39VSv3XTf9vAM8C/1kp9YoQ4gvA/wX8390e\naE+RuBCi697K9Xry8vLyDjV3pxiUpet2RFHExYsXKZfLPPPMMyST3ZVYmpF4uQYLeQCdueXml4wm\nJClH9u1tbmiKUq33SL7i6/hRmtGkSz1XvBNRJCkG8WkUGsGx7m9EAikouAb1W84GFElLkjAlhhYR\nRnUjnGqgobap5A/l3K5S8uNia0tZZCYo6iM0SzQNiUrjdoMeIOwkUYuMli8VQXYaJ6pilzqcnNNo\nnUSu6yjczI3u2NDG3TXSDO0Eczdv3qRSqTA7O9uxYK5UKu2TeDOIhx6JLyulzrb491vALaXUK/f+\n/x+ok3jX2FMk3i3WI9oDBw40VHN3igdB4qurq1y4cIHp6WlOnTrVU/2tGYlfXYSqb7JWaf3+j41H\nsQwncUxBvomYrVMEkWCxlGA87aE1KDVVfRHbJLFG0DXVtNxQh6Dq61R9HWi+mUgYIUE7V51NsL27\nCFVv9ZKAZ49Slg7NnGIdLQQ/nj5uJTRk1P5clZK4mkMhMcVoVELv8vhRcgjZJYFrloOR2Jl6flAk\n3gibBXNhGPLGG29w+PBhCoUC169fp1qtthTM7afTW2M318SVUneEEDeFECeVUm8DPwHM9rLWPolv\ng1JqI6KtVCo9RbTbMUgSD8OQixcvUq1We5pLvhmNSHx+VXB5ycRr0MK0GRlH4ofxiNnybcVsnUEh\nWCo7jCR1rE11cgV4KhOL/WkzWDp96wIARlM+HZeqleJgwoUIInRWtWGQrWv+KbnTCKVXCDuB6sK6\n2LIsSmKMlJXALHfg4Uv9uwvMZPdReHas4e+jKIptnkE/WD+P7YK5Wq1GsVhkeXmZq1evApBOp/nW\nt75FoVBgeHg4lmOfPXuWQ4cO8dWvfrXv9XYD1KPRJ/6fgb+9p0y/CvxKL4s8/Kv3AaJdOl0IwdLS\nEpcvX+bo0aOcPn06FkXpoEg8DENeeeWV2M51O4kHEbx6rT2BA0zm+hezoRRBB8fqFqtVk5StkTHr\ndfJq4DDIKSqWLnvuO9+MjB3ihZ2nuevGLj6BnaOo0m077qywBMTU/qWbhL3MHlCKip7EGZrGyd9q\n+/IoPdZ9FG4n0Z3GG/FB1cS7RbMeccdxcBxni2BueXmZa9eu8Y1vfIPl5WW++c1v8uKLL/LhD3+Y\nU6dOdX3sL3zhC5w+fZpiMR5dxG7Bbp9ippR6HWiVcu8Iu1q+9yDheR6u6zI/P8/Zs2eZnp6OrSUk\nbhIPgoC33noL3/d59tlnYzvX7Y5tb93ScTsg5umReMRsmQRNe8L7RcXTWXHTKGHhhoOthddD/P7f\nR9bp/EPVkSSiNSqJKfIyvcO5bTtUFJGKcUa6MvpzMaspjcrI8ZYGHUoIAtF93GHlGkfh8HDT6ZvR\nqdGLrutMTk7yqU99ig996EP8yZ/8CZ/61KcYGhpibm6u6+PeunWLf/3Xf+Xll1/u5bR3NSTaQ/t5\nkNhTkXgjKKW4ffs2169fJ5FIcOrUKWw73rYjXdep1eKxn7x79y4XL17k+PHjlEqlWC0gN28EClXB\nxYX2DxVLl+hahOyiHazxOopCD2r0bhBGcOVuiiHHgwFFX46hKNT6X3sk6eN3EYWPOlXycrKpeG07\n7GAVzYhJzGZ216/dDEEUURo6QqpyB73B1LPNQ046hZ5Io1k7XRTX8aiR+GaUy2VyuRwnT57k5MmT\nPR33t37rt/jsZz9LqRRfWWV3QKD2SIy6N97lPWyPVqvVKq+99hqFQoFz586RSqUGkvaOIxIPgoA3\n33yTW7ducfbsWQ4ePNiT9Wqn+P41oyMv8SNjYdN2s26gayKGQSmtoQlBxdOYLyQoFt3YFNnrUEoR\ntJmC1hkkjtEZKSoFpi5wQ73tVLl1GASk9Xh6whUQxViakDKinJyo94BvPo5mEvRwqTerha+j16Ej\ncaNXEu9H2PbVr36ViYkJnnvuuZ7X2K1Q7Efi72hIKZmbm2NhYYHTp09viEP6HYLSDP2S+NLSEpcu\nXeKxxx5jampqYzMyCDtXgLlljcVi+wtxNB1R9RWbU8eaUPWpXkoQSUGlUiSdSRG1ILe0HZ+YrRl0\noVgs3v+cSmEOrRaRSYSx1c5SlmIthlr4RDog6OByEQiqoU3OLnU17TOjSrGVinylo8e88VVKUTHS\nOEMJnPw8AEFmjI7TDPegp3JoZutM1aMeiffTYvatb32Lf/mXf+Hf/u3fNgR0v/RLv8Tf/M3f9Lzm\nbsJur4nHhT1H4sVikdnZWUZHR3nf+9635QYelACtn+Eq58+fRynF888/vyN1HsdM8e2Q6PzwevvL\nQiDJJSIqbkDFDTCsNLXQwN8hTBuhsAoJS5FNSCxDIqXcGJSiCRWLirsd/FDbsZEouDq1QDCZCzbO\np3coqkH/ZKAJiS5C2mXSBTp3Kw7DCQ/ZhXFKWvfRvBgEDNRbyrQBRrE1pRONHMMpL3W/uRYCK9ve\nUfFRJvFKpdKTb8U6Pv3pT/PpT38agK9//et87nOfe8cQOAikevjf64PAniLx9YElTz31VMM01G6K\nxO/cucOVK1d4/PHHmZycjG3ddshzrLW4TEmSlsLSQ64v28C9jUWbkr/rC1xfB+oPqqSlyCQkjhlR\n7MPYpROYmmKx0Dhb4YUaN1ctpoeDvoxRk5Zirdo/oU1mfMJWX6mCUNncLRsIFCNOhQ5aswEQSuGE\n8fmjCzuB6EWR3gWCSFLLncD2VtGizjcfRnoYobd/vD3KJL7fJ94c6+n0vYA9ReITExOMj4+3nTYW\nN7pZ1/M8Zmdn0XW9YfS9GXFH4oWqoMR0039PGRErRUW5FJHLGn0JsKu+QNcEt1dNRjMKxwwJY6kn\nb4NS5NuQq1KCm6sWk9kAw+i+113XFMUY0uiWLpGy+XUihKBQc6jcG9hyZKhC1MX3P2S4sfmjY1q9\ntZR1CWU4VAINVx8jq5d32Mk2hKZjZkbav47dVRPvtixWqVRic2z74Ac/yAc/+MFY1tot2E+nvwPR\nLtJ+mJH45tGmTzzxxEZfaL/rdoPXrhlbTbXvIWFElCuKy0v11qnjUxG+6lfBrwij+o22XBJowuTg\ncEQkZaw3n6FD2evsIb1YNMklIrKJENnFOcRl7DKeruE3ufwUBotFe0P8Z+kRju62bSVbh6lFaN5W\nBbISOkq3kJqJ1EwUAl36aEEFTTW/rupjHg22+6PHDQXUSAIKqSBPmnTCxnbvtvx2zOwoosPo+lGO\nxAehh3mnQCGI9tPp7zy0E/Pouo7vx1Mv3L5uK7Kt1WrMzs5iWVZHo03XEWckfnVJY2mbmM3WIwJf\ncXXpft/z0YkAX/XnYAcwmpYsFu4/tKQS3Fo1SNmK0XSIH8PeJAp9lirdbTYKrk7F05jKBShUW1MY\n24jH2CVthQ1bygQCN7RZq269VY8OlzsWsynA1sFzRonQ8ENFJLlPdFuGrCVAT2DpYIoII3LRgsoW\n0mznjx4XIj1JEG39TMqhSZg4SLK22HCjIQwTI9X5MJFHlcS7nQGxF7Efie9BDCoSb0a2Sinm5+eZ\nm5vj5MmTjI21bofZjrgicS+AH87dvxQEEgvJ3B22DONI2gph2E19uDtFwpIsN1G/VzxBxTMZz0bY\nRtRXil3TLVQPl3goBbfWLFKWZDTTWvRWj4z7f1jkEv6OKDxSFitlc8fxc7YPsrPNZkgSTUgqwea+\na9Eo4bIFfgQ+OpBGmGlsHUx8tMCl4yJ8H5BKUQ50tAa8VgshtCbJRGvo4dZ+cjM31rXyPu45372g\n17T+bjj3XQnFvrBtL2JQNfFGN5rruszMzJBMJjl37lxP/s1xReI/nNukKg9dXM/gdoNhJ8cPCPJu\n/w8NQ6OtGvxuUUfXNA4ORQSy+zq1ISTzhf6McCq+RmXFZjQdkrSjHX3sCVOSd/u/hUZSm4xdFChh\nsly2mm5gDmTLtL5MBSEJCjUDUEwkqx2n3RtBqTpx1rAwzCQCiRPkEf3u5lpA2kNoLdT+oYQ1MUTW\nsrH8PNB8yMmjgP1IPG6IHdMA36nYUyTebtc6qEh8M5RS3Lx5k5s3b3Lq1ClGR9u3wTRDHJuOxYLg\n2t36wyNlRly7qzWsJR2dVDERltyRtm+GSApurhoMJSUpO+y8DUypewQWz028UjZYq+hM5UKEdm9D\noRS1GFrKBBJHD+pRuDBYc62WM84PZqrNv3MhCFWdvNc3HFNpFxnF88DXNQ03ANCoiREyhoceFGNP\nWiph4Hb02QqKKokMfcb0Kq4y0Xw/VhfDB4VuSdx13b4HM72TodiPxPckBj0ytFqtMjMzQzqd7jn6\n3ox+I/FIwqtXjY30+eV5QaNLwjYUhql3OzhqByxDke/BWjVf1ah6OmmziOW0V+MahqBcjFdxLJXg\ndt7ENiQTuRDbVLHUwicyAWGkU6jZbYlLF5KMXW1QC9cISFB09S3ZgqQZIrtoy2oFpSDa1LIjFRQC\nG9sYJ6kKXbV/tUNgZlBdXGtaYogSKarlVebmFwjDkEwmw9DQELlcjkQisevTzt2SeKlUIpVKDfCM\nHn307/3waGCfxDdhUJG4Ugrf93n99de3OMT1C13X8bzep1Cdn9fxAvBqktvF5hf849PxpNFTluJu\nqbfdsR/prEVDjGll9BZe2LpQLOYHp9j1Qo1bywIkpJyQpKOhaYJAdl6fVDJEKImpG+Rdk0qH6vlj\nw2Xkpry4UiC1BGuu2SB1KBmyq617zruAaRr3ovCt8ELwyJE2I6xgDdFnF7rS7Z5m0o+N5jAn6/eV\nlJJSqUShUODy5csbUWsul2NoaIh0Or0rxGyb0S2JVyqV/R7xFlCIfWHbOxGdqNPjjsQrlQozMzNI\nKXn++edjbQnpJxIvuYJrS4I7yxKvhbnL9Fg8EedQMuJuqb91FIK71QwTho8maKgcDyJ9MP3mm5C2\nFXdLDm4ZKNd/p4mIjBOSSQoMXRCpOskaGqAUYSSoBYJyTaMW1DchJ6b8jgk8bQVoW8aGalRlimqt\nMRmNJX3CmARoQoi2M83LgY6hjZHWquhhpedjeVqKbgv4maSJadz/HDRNI5fLkcvlOHLkCEopXNcl\nn88zPz9PqVTCMAxyuRxhGBKG4UOfKa6U6mpjUSqV9km8DfbT6e9QtJopHieJK6W4fv06CwsLnDlz\nhosXL8ay7mb0c77feVtw6dZW3/PtMHWF4+h9jwfVhaTchGx6wVLRwqbEUEZH6Pc3RZYONwuDNe5I\nmhHLpZ0bMal0Cq5OYUMsrRCCpuKajO1T9Tv/TKZzpQ0xm9Js1qp203ShoUUY1PpyoNsMTTeQQXti\nDSXkZZKEmSARriFa9Jo3gjTTXU1uA9AE5FKta+BCCJLJJMlkkoMHDwJ1S+O1tTUWFhZ4/fXXUUpt\nEH8ul8Nxmmd7dgP20+ltoLreCz6y2HMk3gpx1c3K5TIzMzOMjIxs+LMPYlhJr5H4zA3BW3PtCeTJ\nw/Gk0ZNWyFo1XrGRR4Z8NWIoWUPoFkpG3GlREogLUqoO03Si5ZC0kUyEJzvbcBy4J2ZTgK/SFCut\n/248WWujXu8cuq5T64DAN8MNBL42QlYroUWdjeBVQuDK7u+NXNpC07r/3i3LYmRkhFQqxXvf+16i\nKKJYLJLP51lYWMD3fVKp1EZdPZVK7aq6+r7lamvsC9v20ROklFy7do2lpSWeeuqpLcMJBpGq72XN\nYiXkf77R/ms/NBpPGt3WqqxVB6Oi9SKdu+Ukh0ZCpNAJ1GDdq4YSEXfy/d8yGWMNT3Y2uEIXkqxd\nRSqTgpdoO/Y1awdEUTx2qEpB2KM4KJKQJ0PWNDGC9rOqIzNHt6dt6IJ0ovfvfLPRi67rDA8Pb+hV\nlFKUy2UKhQLXr1+nUqngOM5GXT2TyTxUu9b9mnh77JUuvD1H4q3S6f2gVCoxMzPD2NgY586d21Hf\nGgSJdxuJr62t8c+vQCDHW75O1yTJpN63laiuKfxosMQqlWApryHUuu3YYHbfulAUelDWb4cmJNms\n03GH9dHhMr5MsOa2b5kTSFKGG5sXi2UaVPvYDyigEDikTRMrWG169kozqPZQshnO2H1Fx63EZEII\nMpkMmUyG6en6PIFarUY+n2dxcZFLly5tqb3ncrmeW9t6eR71O4b0nY5929U9DqVUxw8HKSVXr15l\neXm56XQ0eLiReBRFXLp0iet3DVa9U21f/9hUSNXfSb6GJrH0+sPZ9Wnos74ZuYRkqThYEldK4rqS\npYLGeDbCtCOUiP+YWUeykO8/8jo6HuKGnT3sTeFS9gx82dltOpH2iGJicE0TDdXovaAc6DjGOMlw\ntaFBjK9nurZhdyydhN3f46tby1XHcZiammJqagqAIAg2UvA3b97subWtF7e2Uqm0cR77aIzt5kzv\nVOyT+Dast5l1UrsuFArMzs4yOTnJCy+80PKB8LAi8Xw+z+zsLBNT09yoHm+75ljaw4tMUmY9sg1D\nqPmCkgu1TdGSZShGMhGOrZBKq7cFbSL1bKJzU5d+kDYlV5brx7lb1HDMkIPjEW4YX6rTMSWLhf7f\nS9KK8KLO1jEIydgRvuyM8JNGiIp6bzfcAWHUveNjQi2EUBshI4pom85TGcm2yvdGGMr0r7Ho1zfd\nNE1GR0c3DJuatbatk3qz1rZeSLxare6n01thX9j2zkWnbWatSFxKyeXLl1lbW+Ppp5/uKK31oCPx\nzef4nve8h+9czlBuMbdbE5LhREQQaSysrD9Qmj/g/FBwZw3WU7y2eY/UrXo91As04nJMawZDk9xa\n3vq7WmAwd0dxbCqkGsZ0eUc+UvWvVp4cCnDD1ptDDUkYCkwbpOiUqCRDTnw94YZh4HYpZusEoYS8\nyJIzXPSwXM/o4ECXm4V0wsAy+t+kRVEUa794o9a2arVKoVDg1q1blMtlTNPcqKtns1kMw+g5Et9P\npzeHAuSAW013C/YcibdDO8OX9cj24MGDvPDCCx2n3R9kJF4sFpmZmWFqaooXXniBWyuCN683O886\ned9eCpkasiiWerskvECwsFr/78mcRKoIy9TwO4w8e4EMArxg5/lGUnDldn3iWoCO6qNOnjI9Vsr9\nE3jOcXEDs+W+xtQi7hYMIgnjOZ+ow4dQQq0SRvHcygJ6iow7hVKQDxMI3yftWIRdWsIKAbl0v2Nw\n65BSDlScJoQglUqRSqW2tLbl83lWVla4evUqUE/T+76P53nYdmfvbV+d3h7djBN+lLFP4tvQjGzX\n68rFYpH3vOc9XfdoPohIfHN9fj1DEEbw/72u04g9hhMBd1dDLizC8YN632YsACNpyc1lAIGpSyay\nVSI92bZ+3i1M5XJztXWkOrekMZ6LSCQgkN0fX0NRC+Kor0sySUXY7KGiFIYGt5brM72fPuwSdEjg\nphaRdYzYlLiaYXbUE94vAi3NWpTE0apdubzl0hZ6Dy1ljfAwxpBalsXExAQTExNA/bly+/ZtFhcX\nOX/+fMetbfvq9NZQiP1I/J2KXoagrK2tcf78eQ4dOsTJkyd7UsTquk4QxKQUuofN57Gujh8fH99S\nn//2BY21yrZRlomQYjHkwmL94elYYDkWgdffRW9oikoN1jcMQSSYX0uQMKrk0grMmB46KuJuvrOX\n3i1opGqSiVFFrcs6eS4pWVjrf2MzPeIR0jjCMjRF2dXI35saN5ENCWRrE57NGE3c91JXgNAMQEMq\njSBS+IEiigI05ZG0dYwWaWhD1waSRm+EqieQhomvZ8lZFVDtw39T18j00VK2Hbthlriu6ySTSYaH\nhzlx4kTHrW39RuI3b97kl3/5l1lcXEQIwUc/+lE+9rGPxfjOHjIekZq4EEIHXgPmlVL/qZc19hyJ\nt8Pm6DYMQy5dukS5XOaZZ57pa2qQruvUap0ZX3QDpRRXr15lcXFxR2/6wip8/8qmgRhWROgFXLy+\n9eo+/ZjN3VL/u9aRjKr7im+DGyZw83B4PEBpOmEPUfFm6NKjFnaeUq14ght3FEcnA7xIR3aQXnfM\nuuK9Xxiaj6Qxcdq6Yn7lvk2sQHJgOMAL238XAkXKlriRQyAFYSSaD3zQHSIyFCKFEYXIoISlSRKO\nsUFiSkHwgFpyNE1HGvV6rh8JVmopRhIeQra+P4YzVqyGK7uBxGGrsG17a5tSilqtRqFQYHFxkb//\n+7/ny1/+MoZh8O1vf5tcLtfTJETDMPj85z/Ps88+S6lU4rnnnuMnf/InOXPmTNxv76HhEVGnfww4\nD3RmHNEAD/8K3mVYj8RXVlb43ve+Rzqd5uzZs32P/RuUL3u1WnfzOnfu3BYCDyP4Hz/UN2w/hxMB\nt+/43FzaSuAnpuNJo49mdorMtuPmXY2lFUnSCED11gpl6yELa90rkyMpuLqgUSxJkkb7qM8QquOa\ndCscGVc7STzy8GsRc3eNLT7vTx4IOqhHK3RNo+SZhFJQ9nW8UOtwYpMgxESaI9T0MfJBjlJgU/EU\nFTc+YVwrKAWVYOsGTCrBctUhINW0LJCwdZw+W8q2oxdB2SDQrl89kUgwNTXFyZMn+ehHP8o///M/\nA/CjH/2Il156ieeee44rV650dcwDBw7w7LPPApDJZDh9+jTz8/P9vZFdBEVdYPuwfjqBEGIa+Gng\nv/XzXvdcJN7JTv7mzZsYhsF73/teEolELMeN25d9bm6O27dv4zgOTzzxxI7XfOeCxmpZoAlJygi4\ncH3nlZV0QDMt6HOKpKkrSlXoJAXsh4KrC4KxTEQyqfA7tB6tQ1Iqq77sFEtuvV1uaijASWh40c7j\n153Z+n+4j2cjqsH9dQxN4fuKpWKC7Z9V0grR9ahp9CCEQgiD1YpOEAmOjdZ6mva1GQqBL21M3cJT\nw5j4COUN1F5U0228Jp7x+ZpJ0sqS1Mr3zHvuYzgmMdtmSCkf+uAT6H4zMTY2hpSSz3zmM/XhNJ7X\n12bk+vXr/PCHP+TcuXM9r7Eb8Qg4tv0Z8H8CfdUZ9yPxTVheXmZubg7btnn22WdjI3CIj8Sr1Sqv\nvvoqnudx7ty5hjfvnTV47YogYUVENY/LtxpvDU8es3H7dGUDGE7Jlu1rjbBc0lhaUySMzj+TpB6x\nWo7nkr2T17hxR2GLAG3TqBBNKIoxOLMJJJmkBAS6UGhKcXtFv2d+s3P96aFiQwIXKDRNZ6Vis1g0\nCCLBaCrs2s+8GZRSKFWP5NdqNpUoTb1MFz+EEBRqrUmz6msU/AxKu1/7zqZMDCP+R9VuTKd3gu0O\nb7Zt97wZKZfLvPTSS/zZn/3Zlkzeow6l6tm3h/UDjAkhXtv089HN5yeE+E/AklLq+/2+14e/Dd0F\nCIKACxcuEAQBjz/+OLVaLfZopF8SV0px8+ZNbt26tWMm+WaHufU0+pATcm0+xGsSrZ08Gk8afSwj\nubXS24Ow5guu31Ecm/Bx25ia2HrE3FK834lUguuLgqQlOTAmqQQauYSKx5ltIqIWCAwUC2t6y9T8\n0bEAzdy6YZRRRNX1cFUWNpGqJiQpK8CPKfWdtARF7/7354UaXpgka4eYoka3PdytECqnozplEAlW\nqklGkh4mHtk2U8p6xaNK4uvo9xkVBAEvvfQSH/nIR/i5n/u5vtbajXjIkfiyUupsi3//APC/CiF+\nCnCArBDib5RSv9TtgfYciW+/8JeWlrh06RLHjx/nwIEDrK6uUi6XYz9uPyTuui4zMzOkUqkd0fd6\nr/j67155G4Kaz6Um0TdANgUh/T8YbUOxWpLQRLjVCZQSXFvUGXJWcdK5LYR1/zWSalUS9SmIa4aq\nX+8rPzQSUq5AwqhP4uq1Lc42IqQU3M3rbQeWmIYkmwwJNl0api5YqiYISe4I2nP6Mn4Uj8pf16Dc\nJLVd9Ax0kSLneCCDRqPbu4KmGV0N1FEIVqoOJ8Z1tAGl9+M2e+nnPPqJxHuBUopf/dVf5fTp03z8\n4x/ve73dhnpNfPcK25RSvwv8LoAQ4oPA/9ELgcMeJPF1+L7PhQsXkFJy9uzZDZOFdmYvvaIXEldK\nMT8/z9zcHKdOnWqoQl1fV9d1bq8oXpmJWFxrfZMfP+ywEoMaXVcVSkE8M43ztRypqEomY4G+tf6Z\n0AOuFwd/qZaqiqW8ACJsUzGahaRTJ3M31HbU4pWSJEyFISRSKjxfUazCyJTOjeXOzvfUQX+DwIVQ\nRNLkdpOZ6EOJENuMz6XL0DVqLZTwkRKsug5J0yRp1FA9ihGVVBT97r+/tK0YSg7uQTxos5dO0S2J\nd2MK0wzf+ta3+MpXvsLTTz/NM888A8Af/dEf8VM/9VN9rbtroB56JP7AsCdJfHFxkcuXL3PixIkd\nQwQGoSLvZd1arcbMzAyO43Du3LmmNa/1SDyMFH/3P0MW11qv+64TJiul/qOPhCiQr8VbQ6sESVRF\nMTly3/tcUz43Y06jN8JkLmJu8f5xvEBwe2X9/ySaiBjJgG34uK6H0pKUajrhlkhbcHgCViud3VZT\nuYAgqtfNDV2wWrGatpcJJLlEZ+1nnSBhCYod6hiqgY4bJBlOhCBrXUflodIJVbePGsWRkcHK5R/V\ndHocE8x+7Md+bCDTHHcL1tXpjwKUUl8Hvt7r3+85Eo+iiJWVFZ5//vmGowMHFYl3OjZUKcXCwgLX\nrl3jySefZHy8zdhQXUdKyf94VbYl8PEhQbmBTWm30IWHKwfjFlX1BHOLiuOTIZXQQEbGGHt/AAAg\nAElEQVSDHylo6fJe9qI5O0klWC4C2Pd+dkLXFLZjEnYwh0QIycRQiB+CEDoLhcaueus4PNJJ+1ln\n0ARdj5lVCFZdk7StY1Pp+O+E0KhG3QtEJzKKxGBK4Rt4VEm8VCrtu7V1gEeFxPvFniNxwzBaGhoM\nKhLvRITi+z4zMzPous4LL7zQ0SQ1TdO4dkfyzR+1vmI1AVMT9g73tl6QTRos5geZ5hRcWYCjYy43\n1gZ/iWYTklsxfC4nj2isuZ2RwulDAVJCNbCoeK3/JuOEBGF8TyS/VkGZvWVRyp5GYKTJmC5Ktb9P\nvMje8CroGDKA6gIVO0cymRxYy9ujWhMvl8td2z7vOeyn09/ZEEI0TSXpuj6QSLwd7ty5w5UrV3ji\niSc2fJU7QaR0/u27ZtsL9uknTFYq6+5ckoQFti7RhCKMFFEEtiXwI42K3/yBMpmLuLk8+AefbUh+\ndDliOBNh2DZeOJhjjqSjhi5zXa+ToW371DqGkhFCg8Wi1VatLZCMJOOLwh0TSrK/MogXCoIowUjC\nR8nmJgOaZlH1uq85T2V8pBtx7do1KpUKyWRyw3a02TjPXvCo1sT3fdPbQwEDiMV2JfYkibfCg96Z\n+77P+fPnUUo1TfG3wg9vTLLWpnf68LhCRoqk7lOpKQplWG54gStAYukuB8ctDF1RrikiUZ/ilbYV\nC2sPSPEZ+tR8WFiBTMJjYsyk5MV7uWpCUnE79ylvhckxnXwH/eW2ETGckdwpdOYBPj0cH4ELoBbT\nZqjusmYxktQhchvWyUt+9z7naVtyaMwGDnP48GGUUriuSz6f3xjnaVnWlnGevRLxbkmnb24R7QT7\n6fTOsB+J72PguHv3LhcvXmwosOsEF29J3l7INf334ZREBR5+lOLirc6vaD8yuX5n/fWCXMpjNAum\nDmE04EIlMJLwuTB3/3xLLrjzAY8flqy68R0/IQqsVPoX5z1+CPLV9kSSsQPSjqLYYcSedkLCDnQU\nncLpQszWGQSrVYOsk8LcVidXWqJte91OKA5kfYJAoZRC13WEECSTSZLJ5MY4T8/zyOfzLC0tcfny\nZTRN25j6NTQ01LHxyW4hceiu53t/DGl71M1e9gaL70kSb5VOH/RxpZREUcSFCxcIw3BLe1s3cD3F\nP/xH43xRNhGhRT6XrwScfSbL7T6j50IF0k7E23Nw/EANT1kDmxNuG5LrCzvfVyjhwlzEiUM1yoHV\n14xwgIwTsVrs/0HoWIpQtN5YaEJiEbK8BslDOnTEy5LRmNPo8RL4fRRrGo6ZJm1UUUqiaQarHWoD\nNmMyC7mUiVKKKIpQSm3cL1DPkgkhsG2byclJJicngbppSaFQIJ/PMzc3h1KKbDbL0NAQQ0NDTbNb\nSqldQ+LdoFKp9K1O3wvYj8T3OLpNcXUCXde5e/culy9f3jCX6fUY//LtiMI2kXDKliQ0n4vXfaSC\nk8cdbscwSnMkLbmxWE+2X11QJCyPI1M6K1UDEfOc8PU0ejNcmVccGPHQHRu/x9SwUhKh4hlwcmJa\nZ7WFKC5phqwWJHeqgudPQ7lDVfjhmNPoXqQRR9mgGWqBwAschu0a1dDu+limrpgeuV/OWk+RSyk3\nyHz9Z53UhRBomoZpmoyNjTE2NgbUa8zFYpF8Ps/8/DxBEJDJZDZI3XGcgfrDDxqlUqmnyWV7CUrt\n18T3NLa7oMWBMAypVqvMzc3x3HPP4ThOz2u9eVXyg0v3t5mmHjHshFya8wjuPfgzSQ1lJaDP6ae6\nJuszqTdFj64Pb9+ImByOSKXiq1VvT6M3w8JqvU4+OWZS7OHYUzkVi4Xr9BisVppcI0qStiKu31FI\nJTh9RFHu0PAkZUdb0+gKNF2gCUEYhJSrLolECsfSiKRsOzc5/jR6Yyh0FguCKKqQ6jJSPDJad5Db\njlakvh6xbyd1IQTDw8Mb1sRSSkqlEoVCgUuXLuG6LqlUCt/3N5TeD4vUe8kIlstljh49OoCzeWdh\nv8XsHYx2N+x6r3hcJL66usr58+exLIszZ870ReDFquL/+eb9LeawU+XGfMBCsPU9nXwyw0KbvvFO\nMDWsuLbQ+N8W10DLBzx2MKISmn3NCW+WRm+GkgvV+YAnDsuuMgIJS3JntX8xm4ZE6Aoa2NdaeoTv\nRVxdEIAgnVCYjr7FWrUZTF0ylJCE0iSMBF4o8MN6n/a91UEk8Wrc26Ap0rYiaUkEEUGktojMbGNw\nafTt0DVFQeWIEIhaFdtU6Hr7R0wuoRjtkPMbkTqwkX5fJ/QoihBCbPzkcjlyuRxHjhxBKUWlUuGN\nN95gbm6OcrmM4zgbkXomk3lgafZefNP31emdQe3XxPcu4uoVj6KIixcvUi6XefbZZ7l8+XJHhi+t\n8N//I6Lq1R+YI47H+ash2wnp3aeSLKz1/xBKm2WuLTg71t8MqeDyvCSd8BjLSSpRj/2rbdLojRDd\nq5NPDkek051lBBKmZC0G17NTx3TW3J3qayMqsrhmE2zSDJw+Jtqm0W1dEkaChKFYKnVzWwrKnqDs\naYCBoSkyjsTSJUpFBHKwafTNCCJjo0RRCZMoIcmaQcuISKA4NBQA3SvZ4T6pbybd9ZT7esQO7Kir\np9NpLMviqaeeQilFrVYjn89z+/ZtSqUSpmluCOVyudzAWtF6IfF9YVt71IVtD/ssHgz2SbwB4nBt\ny+fzzM7OMj09zalTpxBC9L05+M5MxMWb9Yd0rexy/vbOtcaGdUpB/7OXLUMSqM6dtsoulF2NY1Mu\nNWl35bI2nPB5u4M0ejMsrsFSPuCxA2FL0d1ENuJGDGn08dzOnvC0FVIsR9wubv3MpkerlP3mD1xb\nl/iB4FZeJ5uQGEZ/5xdKwVpVB3SyjnFvDnnYveFKl7B0wZ3iVjKqBhpeZDGRDgibREW2XOH8W1eR\nUm6Q5vDwcF/e4Jqm7SD1zT9QF8Otk70QgkQiQSKR4MCBA0C99TOfz7O8vMzVq1e3RPNDQ0MdGTH9\n/+y9eXxcZ33v/z6zz0gajUb7ZlleZEuybMd2YpPFsaAk9/KjwA2Uwu+WJE1CWnLhJqW0DaTcJqWv\nkgI3QCEsrUlCEkhioIEQkrS2icm+Oo4tyVqs1dql2TSjWc85z/1DmbFla5lVkq15v155kYiZc56Z\nOed8nuf7fL+fbzwkK+LZxLbFUbMr8YuXxcLpqYitqqp0dXXh8XjYtm3bLGelVI474Rb87nWVUmuE\n7v4gwdD5F6gkQXV1HuOepE4xi8JcQf944u/rG4USWwiz2UggjsQzk16lb47JSKIIAd3DApMhRE25\nFldAB2dlsBt0KhNuddbfkkFCUFigwxOYuYZyDDJ+v0rPpHTesc0Ggd1uITLHisCoUQhFNAy6o7eg\nSqlNZXqermKJYjaoTPq0CCQMOi2FuRFkJTMPNY0kmJynra2iSoxMGSixyqiKPOveM+kFW6oK0UiF\nKIoSyzA/OxkturedSjLauaLu9/tpaWmhqqpq3gx4g8FASUlJzHhJluXY+E6fPo2iKFit1pioJ7tF\nlmw4/WLq/Z0JhIA0VmeuaFaliC9Gsitxj8dDW1sb5eXlXHrppec9dJIVcUUV/OKITL4hSGvn/DHn\nHY25jHpSX3FV2FX6RpN//7gbzP4AFSV6pkLzl18JoaKEQvP2PE+GYBg6+hWK8hUK8vWxFbNFG2Q0\nnHqEom6NBk9Ai1mvEAkp9A7P7HvPReM6ienI7Ae0QYrgmVaZCM9esa8tjjCdRKevuRFEFE1sHz0s\nS4y4DdgsCiadTLq1PBCIIIuFv9vxKR02s4RRG0F9b1xri2bsgGHm3rDb7djtduBMMprL5aK9vZ1g\nMEhubi4FBQXYbLakk9GcTicdHR3U19djs9li51osA16n01FYWBjLClcUBa/Xi9vtpr29nXA4TG5u\nbmxf3Ww2xzW+ZBJos+H0eBCoq6TGbFWKeLpX4qqq0t3djcPhoKmpad5QV7Ii/sIxmaHhaUbntlkD\noLJUz8R06iE+s0FlfJFWpvEQCGvoGYpQlj+FrC+a8zV2i0xHf8qnmpNJD0x6IqwtiyBJYUY9qYcf\n8y0CRWgwEKZ/BBbaa95QIZg+q9mMViNQZRiaOl/scgxhwoqUtq1rqwkm5nDxc/u1aCQNJVZ55jpM\nQ0Z2JORnWrHF9Vp3QItJr8FmDmOzCKwL7NZoNJpY+Hrt2rUIIfD5fLhcLnp6emJ2rNHwe15e3oL3\ntRCC/v5+Jicn2bFjx6xwfTwZ8LIsx5Lkoqv1qGBH3zM9PY3b7aa7uxu/3x8bX9Qudq7xJZNAm3Vs\nWxwBqBmKPK00VqWIL0YiK3Gv10tLSwslJSVcdtllC2a1JiPiPUMRfvlfUwsmfWk1AntxDk5vQoee\nkzyzYNCX+nEAhNAw4s5hTYmPoDAjOPOwMmrC9Ayen5SXbgbGZLSqisEwjd2qRafXEJC1+Bfwhz8b\nraSSa1TRaVTy83X0jaiL7i+bDIKcPC3h9y4hs05lzK2dp42oSkWhlL4wun4mjD4fqpAY9ejJMWix\nmiOk0ldFqAphkdjkKBiRcAkDTVVxtHo7C0mSyMvLIy8vL5Zh7vf7cbvdDAwM4PV6MRqNsfC71WqN\n3YuKotDa2orBYGDHjh2LZp4nmwEfHV/ULjY6vtOnT8fsYqOiHh1fMuH0cDiccj/xix4BSlbEVy/x\nNEFRVZXe3l7Gx8fZsmVLXDNjrVZLJBJ/7DgUFvz7k75Fs7brajU4vamLYWWhOm85WSoMjGsps4fP\nNDIRKtO+AJElsHAttar0jmghAA6PAihABKsFigo0GI1awqoWf0jCYhAYtApCVQmGBB6fyoR3ZlZf\nv05P/3h8D9st6ySmIxKSJNAKGJic/zZbV6qkTcBBIKuas8rR5mc6rGE6bKA4V0HSJJf4ptVoCSmJ\nP0I2lckYUnzySJJETk4OOTk5VFZWAsQ81oeHh2lvb0en05Gbm4vD4aCmpoaqqqqkzpVsBvy544tm\nwI+NjdHV1YVWq0Wr1WI0GpFlOW672HPHkuV8BCzqn3CxsCpFPJ468VBo/pWCz+ejtbUVu93O7t27\n476htFotwWD87iuP/9c0486Fl0prK/V45dTbEuaaVIYnM3fVjzoh9z2DFg0KnROZF/DifJW+kbl/\n6yk/TPlVZjxQF55Y5Vkkgmp8413/XhjdpFVx+jQLthm1mpW0ubIB5JnEgqvw85GY8OkwGzTkmyIJ\n7ZXrNTDuTXz7xp6jUG3PjJXWuRnmIyMjnDp1CpvNxvDwMMPDw7Hwe6oZ5vFkwEdFPuoBbzKZKCsr\ni/VJiEQidHd3EwwGOXbsGMCsDPi57GKXwy76gkRkw+mrmvlW4tF9teHhYRobG8nPn7/5yHzHjTec\nfqwjzAtHFw45Gg1gtuYwNVf3LCEw6kVcLTyFUDHqBc6puIaWNL4A6B1BDFqFuUxS0olOI/D5FNJx\nG6+rMTE+FUeHMr0gL08DqsqgQ7vIilgl3+xHwZKGEYJGBJn0mpLanQiENYRlA6XWCJF4HnxC4Avr\n41rxzxqjJGiqynybXyEEvb29uFwudu/eHRPDqMe6y+Wir68vVtYWFfV0l7Ut5gGv1+uxWCwUFBRQ\nWlqKLMsxu9jBwUFkWZ43Az5Vh7nnnnuO22+/HUVRuOWWW7jzzjtTOt5KJFtitorR6XTniW20LCU/\nP589e/YkFc6KV8Q9PpWHfrv4xvTWBisTUyoGdRqdRiUUDKLVmpgOgMOtEJEhP1eirFiPyazHL+sJ\nyuev1KqLoCcDYfRz0UgCjyvA6KRC/ToFZ8i0aD/tZCmzqZwaTP04dWv1jE/Ft7ptXAcevwaPf/Fr\no8jsRpESmwTOixDo9CZIoSmNokoMu/WU5cvI7+31zodep8UZx2c8lw0lMrnGzD5YZVmmpaUFi8XC\nJZdcMus+nctjPSrqg4ODRCKRWOOUgoICzOb4fRLOJV4P+FAohNFoRFVVdDrdnBn6brebzs5OHnzw\nwVh5W1tbG/X19UmJuaIo/K//9b84ePAgVVVVXHrppXzkIx+hoaEh6c+70hBCZFfiFzPx2q7CzMVw\n+vRpBgcHaWhoiGWjJkO8Iv7Qb314/fNfgDM9l6H1pAffrNfpmdnzPYPHJ/D4wsDMxnpJgYbiQj1a\ngx5fWI/FBAPjS3OxF5pCtA7OjO9kT5jqMgXJaCEQSe/+XrFVpXso9SLRHDMoi3Qog5lIxrpywZDT\nGFdTFYMmiCknL217dlaLYGKeOu3EmEl6s+do0EoR5lrW6zQkda5co8r6ksx2pPD5fLS0tLB27dq4\nWvvOVdYWXQmfW9ZWUFCAxWJJqVY9es7ouYaGhvB4PFRXV8+ZAQ9nwus1NTX83//7fzly5Ah///d/\nzz333MPJkyfZuXMnDz74YEJjeeONN9iwYQPr1q0D4FOf+hS/+c1vLioRB7IlZquZqNgGAgFaWlrI\nzc1l9+7dKVsvxiPiz78V5HjX3Hu0ZoNKvj7AqZ4pdLqycwQ8PsZdKuOuEBBCqxFsqtFh1pnxJpGg\nlAgFFpmTp2ZvD5weVcjP9VFaZsHlT8/5JRTcnhBCpF5ut7HWzNgidfdGnYpRCiOTE3dXtJpSTdqS\n2Yw6FUdC++CL45zWYtGDSetHqz8ziRFCEIzok4ieCJqqIrGa8EwwPj5OT08PjY2NSZdfRfuS22y2\n88raTp06FSsbi4bfFytrm4+oIVQoFGLXrl1otdq4M+A3bNhAbW0tTzzxBEIIxsbGEj7/0NAQ1dXV\nsf+uqqri9ddfT/g4K5mZLmarw+1l1Yr4Qj3FtVotPp+Po0ePUl9fH5upp8piIj7qUDhwcPq8vxt1\nArs5wMl2Nz1Bld27S+kbS32WWVuh5XhnCJ02xLpqCT/5CCn9l4RWI3BMBOZceXp8guneaTZvMDPm\nTX2fvNIOpwZTF/D11TrGPAuLo90S4fRIhG0NFtzB+ER5xtQlPaI7c/1qMrIl4Y9oCck5lJrk2D65\nQadhbCrxyccau4I9JzOrIiEE3d3deL1edu7cmTY7VJi/rM3lcsXK2qKNU84ta5uPSCTCiRMnKCgo\noK6uLjYJiDcDvre3F6/XGxtfPBGH1coqWYivXhGfj2AwSEtLC5FIhL179yZU9rEYC4m4ogr2P+kl\nfNYiXKcRlOYG6eh00zc98741lSb6x1NfxVlzoG945mSyAp19Anv+FFVVuTj86U06sxmCnHTPPyuW\nFWjpCKS8T15kVelJQxjdZATJYJy3jatWo5KrC9PRp7JprR53MD7hyDEqMbeydJBvntvUJV0oQsOw\nS0++cQqjwcCkN/HEL6NOsLk8M8lsUUG0Wq1s37494+1Ezy4bi5arzVXWFl2p22y2WdG7aLh/3bp1\nMTvXhTg3We7dd9/l7/7u77jppptS+hyVlZWcPn069t+Dg4OxMriLhZloRnYlvqoQQjAyMkJvby91\ndXV0dXWlVcBhYRF/+sUAvWd5iFfaQnSfcnG668wDUKMBsy2X0HTqDytbLjjds6eqTo+K0zPFxrUG\nMObEbYiyEIU5Mu0LWMWeTXSfHKOFYIL75FqNIBBQ0rLPvHm9ad4wutUk43KHOTUFOSawWE0E4yz9\nryxU3+s2NoMQAp0GNO/l0KtixoZUEdKiYm/QClxJJJcljCThCeej83tQdXokTWLXxJbKCPoMNADz\ner20trbGLYiZYq7GKS6Xi8nJSU6dOhXrbS5JEhMTEws6Os6HEIKnnnqKb3zjG/zqV7+ivr4+pTFf\neumldHV10dvbS2VlJY8//jg///nPUzrmSkRNxcnoAmLVivjZ4fRQKERbWxs6nY7LLrsMvV5PV1dX\n2s+p0WjmbEXaOyTzuxcDwMzKJYcp3nr7fPu1bVttDLtTXyXXlEl0n55febr6whgNETZvsOAImBIu\nJYpi0AmGh/0JlXlF98krK8xM+OIPjZYXqJw6vfjrFqOsIMTYXBatQqXQEqHrtBJrcbit3oIrnjC6\nUCmzKfiDEoosCMsQCEv4Q3OHwiVJUJgryDOrSFrm7NOu1cx0LFsKcvQKAx4b+RaVHLMad9/4MqtC\nWX76H6QjIyP09/fT1NQ0q8HQSsBgMFBaWkppaSkwI+qdnZ24XC4MBgOtra0JlbWpqso3v/lNXnnl\nFQ4dOhTzbk8FnU7H97//fa699loUReGmm26isbEx5eOuKMTKNnuRJKkaeBgoZcab5t+EEN9N5lir\nVsSjjI6O0t3dzcaNGzM+o58r3BeOCPb/2ouiQlGezOhpB32O8wW2tMTIhC/1mmKdVmZoTGaxnz4U\nFrzbNk1ZURB7SS6eOXpnL0aOFGDQl/id5PEJPJ1+1lfpiGgMBOSFz11sVekeTE8YPbfAzvQ55fl6\nKYgcjtDef2ZJublWj2uRMLoGFZM2gtOtMqkxEozEJ7pCSEx6JSa9M2JpNgjsuSomg0BGItcomPQt\nza2r0whG3TOf2+PXEAhLlBUoBBfxH9BKChuKfED67EGjCWHBYJBdu3alPVKWbhRFoaOjA71ezxVX\nXBGzWY23rM3v93PbbbdRXFzMM888k9b9/g996EN86EMfStvxVhoCgbqyw+ky8NdCiKOSJOUBb0uS\ndFAI0ZbogVb2XZBBwuEwra2twEx4aS53pKXgl4f9jDpUKvODHDvuQJbnFr2qtcUMjqd+UdpzQgw7\n4n+wjk4qTLo8NG7OZdIff7vF4twIrR2ptSfrHpTRasLU1ZpwhUxzZn/rNILpaSUtSSznhtFN72We\n94woqOoZATcZVIw5BsLz5ChqJBUTEU6PK0wHJZo26HCksAUSCEsMOWfOb9QLCiwKOoNYkpW4UAXh\nswQ7LEucntBSVaQQlKV596FLDGN0d/YRCoWwWq0ptxQNh8OcOHECu90+KyFspRIMBjl+/DgVFRWz\n7F4XK2vz+/3cf//9NDY28uyzz3LzzTdz2223rfjPu+IQK9vsRQgxAoy89+9eSZJOApVAVsTjZWBg\ngNLS0nmzOyVJQlXVjHoUt/WEeflYAJvWw1tH5zd32bG9MC0CXpwvM5KAgEeRFXi31ceWOgV3xLJo\neN2oUxkYDCQ7zFkoqoaT3WHsVpmyMtN5IfZ0mbrMZKPP3A5GnYpZG6F3WEFW4Nx66a2bTXgj5986\nkohglBQGRlWC4ZkWpRWFMyVb6SLPqHJ6UoteJ1hTrBJUNRl7wFv0M+c6F4HE6UkdJVYFjVact39f\nmKuwY50dsM/ZUjQvLy+28oyn9jra4nfjxo0xo5aVjNvt5uTJk2zevJmCgoIFX3tuWZuqqvT397N/\n/35ycnL48Y9/zPPPP8/nPvc5PvCBDyzRJ7jwmelitqJX4jEkSVoLXAIkVee3akV848aNC5Z7RZPQ\nMiXi/qDKk4c8TI1O0OtaeMWqaEyQooGohEBWtAiRvOFGS2eAmgoZbU7egnauJoJ4p9M7C3ZOqTin\n/NRW6pCMJrxBLSX56QujS3ojekUlVxehb1iJdSA7l821eryR2U5eQgmgBgOMug0oqpao6EsI8vON\neALpEVmbRWHENXOsiCzRPSJhz1Ox5UmE49ynjhetJJjwLHzM8SktuSYVW65K+D23OI0kaKo8Oxnz\n/JaiUVHv6uoiEAiQk5MTW6mf2yd8aGiIwcFBtm3bhsWSHovaTDI8PMzg4CDbt29P2PFNCMF//Md/\n8KMf/YjHHnuMjRs3IoSgs7MzuxJPFDETRVpGiiRJeuus//43IcS/nfsiSZJygV8BdwghkjK+XrUi\nvhhR17Z07kPBmRX+Y78Z57XXxljMwK260sKoM/WLcU2Zlu7T8WWJL0T/cIQ8yyQVVfn4Iuev6kty\nI7SkGEZfiN4hGZ3Wx6Z1RiIhCUHq4lW/zkg4EmZkVGF4gaGbTWDOOycbPehi1Gkkopz/wK4sCuAJ\nJG/dORtBRIZzowJOrwaXT7CmWEHVxNfBLB40iLgqBHxBDcGIRKVdISBrqCuTyVnAWlWSJKxWK1ar\nlZqamgX7hLvdbiRJihmirGSEELFJyc6dOxMer6IofP3rX+fYsWMcOnQo5gwpSRKbNm3KxJAvcpa9\nxGxSCLFroRdIkqRnRsB/JoT4j2RPtGpFfLGZbTK9v+NBq9Xy6ttufvVMfE5LVdX59Iym48zpm5V6\n/Rp6uqeorpQIac+EN006hd6B9ITRF0JWwO8L0dEbJj9XQ2mRDqNJRyCixeXTwCK/rUmvkmdS0WtV\ncnN0nDodIRBHe+vt9WeZuihBgtNhxj1z5wnkmQVaUwFqmi6hEqvKkGNuURVCon9cIscoKCtUCamp\nCd58YfT5kBWJ/gkdmyoirCtK7APPZajicrli1SJCiJg5SkFBQdIuaZkkWq9us9nYunVrwuObnp7m\nL/7iL6ipqeGpp55a8Ql7FwIr3bFNmrlIfgKcFELcl8qxslfLPJztn55OIrKWHx2Ir9uIVgvjUxpS\nFWCLcWYFnU4iikTPADTWeXGHc0DSEJqaZDoQf/JbslSVSHT2zaiux6fO8oa3mCTKi3VYLHrCqhZJ\nEug1Koqs4g8oONwKjumZm9ti1lBRbYtLwOtqdDFTFxF0MuE2EYzMH6VZW6XH4UuP2Jh0gnF3HD3C\nQxLdwxLldgWjUYOchGmORhI44ujYNtf7NpfLi82fFsXj8dDR0UFDQwN2ux0hBIFA4DyXtLNFfTl7\na09PT3PixImk69UHBwf5zGc+w2c/+1luvvnmFTdBuZBZ5nD6YlwBfAY4IUnSsff+9hUhxDOJHigr\n4vOQqZX4oVe1OFzxTQ4aNhcwnoa95YpiDe29KR9mTlo7Q6yrFtgKjJwYyryAmwwCp0ueNxvdHxTv\n1cAvPmmp32Rl0BHPOSE330wgHCHk9TLmWThEXlMm4UhjCViOUcUbiF+oRpwajDpBcX4A9IntI+sl\nkZTJz5ZqGXtu8teqEILBwUFGRka45JJLYm03JUnCYrFgsVhirmJRUR8cHMTr9WIwGGKiHo/1abqI\nGrok69f++uuvc/vtt/O9732Pq6++OgMjXL3MdDHLbMOdVBBCvERSjYPPZ9WKeEPBRdMAACAASURB\nVCKdzNJFa6ePN47H/3pzrgXSIOIeb2Yv5tHxEGOnJ7DZCnD7M7t3WWaX6OxLPUy2eYOZwXnC0+fS\ntMmA1+vB4dHjDy++x2226ImkaVfBwBSj7sQFIiRLDDlM1JbJhOO8zc06hUFH4r9fvkVle03ykR5F\nUWhvbweIaz856pJWUVEBzJRzuVyumPWpXq+PZb/n5+enfT9dCEF/fz8Oh4MdO3YkXJ4qhODxxx/n\nxz/+Mb/5zW+ora1N6/iyzLCSS8zSyaoV8cVI90o8FJL55o964k48suXrOD2R+kVYUiAxPJ4Z7+oo\neboALaeCmCfGaGgoYsSTmZr7NaVnwuipkGPRENHEl3BWXawwOell3BufkFYUwVQCq+aFkBBodDnx\nBBXmRCDRMzpT0y3pFk56kxB4pjUkujiQEFxRF0ab5EcOBAKcOHGC8vJyqqqqkgonm0wmysvLY9an\noVAIt9vN+Pg4XV1daDSa2Er9XD/zRFEUhZMnT6LVas/rVx7v+//xH/+Rjo4ODh8+nHTHtSyLIFa8\n2UvayIr4PKRzJe71evneAx2MO+LPdK+rs9M/kfq5rTkSw6kfZl7KCxSOH5+xiA0EVY6+M86ObQWM\nTFkWTTBLBLMRxifTs6+/eZOVwcnFX2fReAmruTjjFHCAQpsOx/mN6JKiKE9l2Jn6hGBwUkNhnkpe\nnmZegxiTTjC5SNe2udhcKVOapLWq0+mko6OD+vr6WDZ2OjAajedZn7rd7lj4O1qbHRX1eBPJgsEg\nJ06coKysbFYrz3jxer189rOfpb6+nieffHLFZ9xfyAhW/J542li1Ih5PdnoolNqqLxp2O9Yyyqvv\nJlZqNGM1mtpFqJEEg6OZK/fSawWjQ55ZfxMC3j7mYvOGMEGtjbCcHiEvzFPoSUNNeEOdhcHJxYRR\nxRAaw15uxxWK3xxHqxF4Q+l7MEfSGEBxeDX4Q4LyIpXwOdnrRm1yk4Vco8rO2sSvr+h9MTk5yY4d\nOxb1D08Vg8FASUlJLPEsEongdrtxOp309PQAzBL1ucpKo4YzmzZtSqo1cX9/P9dffz2f//znuf76\n67MJbJlGkJGcppXIqhXxxdDpdExPJ7+kCgQCtLS0kJuXx5G37ShK/JuktTU5jLtSn0VWl2npHsjc\nhVxqDfNO39wP8fZT05QUhcmz5xFQUjPpKLeH6UmDK1tejoagWDj5zqQN4RmfRBhzmJIT6za1rkLL\ndJomLWa9YDKJLPGFCIQl+kagtkwhJGaEXAhBICQl1f718rpwwh3KFEWhtbUVg8HAjh07liWzXK/X\nU1xcTHFxMQCyLON2u3G5XPT19aGq6ixRdzgcDAwMJGXgAvDyyy/z13/91/zwhz/kiiuuSPfHyTIH\nF4B3etrIivg8aLXapMLpQgiGh4fp6+ujvr6ed9slOnsGEjpGcVku/fGVkS88lgxexIV5KidaPQu+\nZnwywpTXRWOjLul98hwTONwS6ahzr9u4cDa6RZ2kr18mHNFx5d5CJhIUUaNJSwrzvlnkmRSmMpAk\nqIoZp7ey/AA6k4kcg0ioJjzKhlKZSnti15ff7+fEiRNUV1fHktJWAjqdjqKiopilq6IoMVFvb29H\nURRKS0vxeDxoNJq4IwdCCB555BEeeughnn76adasWZPJj5HlbARzdoy8GFm1Ih5Pdnqi4ZhoUxWd\nTsfu3bvRarX85wvdCR1Dp4WROMqeFiPXDP0jmUpoEwS9PmRlcWENhgRH3xnnkm0FjCaxT15oFZwa\nSF3AG+os82aj67UKYdconeM6QGLXJTYmphITNqslvf29p9Jk1Tofox4TedNuXBozaBNbXZr0gsvW\nJ+b+Nzk5SVdXF42NjVit1oTeu9RotVqsVisDAwNUVlZSU1PD1NQULpeLoaGhWOexs5u6nIssy3z1\nq19lcHCQw4cPr7iWqRc7MyvxbDj9oufsnuLnkmhi28TEBJ2dnWzYsIHS0lKEEIyMBznRntjSrLHB\nzqh3RkD0OpU8U4j8HJn8nAhlhTpqKnNAk0PHgKCtJ8K4c+7ZZlmhBndSTryLs6ZQ5u1j8W8PCAFH\nj7nYUBvCkJMfdxna2jKJzr7UrWItZomAOvfqKVfr43T/FNPBmVshN0eDrM+NesfETXWZDleahDff\nojC5iG95OoioFjxTgtKiECER/7707g1hjHHmaAoh6O3txeVysXPnzmXrFpgIUQOX2traWHLcXJ3H\nos5y4XCYvLw8FEXBZDJRWlrKTTfdxK5duzhw4EDaE9huuukmnn76aUpKSmhpaQFmkgT/9E//lL6+\nPtauXcuBAwcWbb5yUbP83ulLxqoW8YWIt8RMlmU6OjoIhULs2rULg8GAoiioqsrhl1wJtchcW2Xk\nv+3NJ98qcI13UVlmpba2NtaHOJqM43L1UlcEuzcWgM7O4KSF9j6Zk70y/uDMCZ2ezMxCTQbByQ53\nUu891etHpw2wtTEfR8hCZIEmKjlmGB5PXcABamuMTJ7TClSvUSAwTsdpCcGZh+zOncWMJrEXHRHp\ne1Drl2CbON8s0z0IIOEfUtm4Jsy0vLjAVtsV1pXEd23JskxLSwsWiyWpcqzlwOFwxCIG85V/nd15\nrLa2Ntap7ciRI3znO9+hp6eH+vp6ampq6O3tZf369WlNZLvxxhtjCXJR7r33Xj7wgQ9w5513cu+9\n93LvvffyL//yL2k754WHyCa2rXbiWYm73W7a2tpYs2ZNzE1KVdXYXszhV+ITu8oyA///R0u48lIr\no6OjDAwMsLVx86yyG61WS2FhIYWFhcBMhq3L5cLlmsSiurm0Vss1O+xMywUMThh45kV/Mh97UYrz\nZE4Hkt9rkhXB0eNuCvJ9rFtfwIhn7hWgPU/QnYbkvvqNFianz4Q7tZKKQZ6kv18mHJktvBvW5TA6\nlXjDm4rimUYg6UAjCRzezIbSNZLKpEshWhOuqBLtfSrrKoLIGsO8TWU0yBh9r9PWZsRut1NQUDDv\n/rDP56OlpYW1a9fO2+53JSGE4PTp04yPjyds4BLt1FZQUEAgEOCpp57CaDTyhz/8gS996Ut873vf\nS6okbT727t1LX1/frL/95je/4ciRIwDccMMN7Nu3b1WLuMiuxFcHC4XTF1qJq6pKd3c3TqeT7du3\nY7FYEGJm5ieEQJIkTrRPL1rXXFqk51MfKaH5chuKPNNEQafTsWvXrkVrV/V6/ayymVAohMvlIuQc\noUDr4dP7zLzZVcKxrvT+xJMT6ZkcuDwybx+dYP1aMyZrPq7pM+NMVxg9x6IhxIyAazUCuyFAx6kp\n/EEJmC3gkiTItZsIJJFdXpifvtpwe67KSBpqwxfCalQ4NXn+5+wZhhJbmFyrnsgcTVQu3aCyuXwb\nU1NTOJ3OWfvDZ4v6+Pg4PT09SduRLjWqqnLy5EkkSUoqY14IwQMPPMDjjz/Os88+G5vQ79ixg7/6\nq7/KxJDPY2xsLGZ2U1ZWxthYGjJjL2QEqHJ2Jb6qmS/8FV1hlJSUcNlllwHEwueSJMUeAIdemn8V\nXlig408/XMIHrypAp5NwOBx0dnayfv36pJoowIzBRVlZWWzVEwgEWLvGyaYqF//1Zg4uX+p7kYV5\nKu1twZSPczbdfQG02gBbG224QxZ0ek3awuibN1kZcQiKzUG6e3z0T6vM50i2bUs+ATnxUjidVjAV\nTF8oPQM9d2Zh1iv0jc7/PYy7wRcIU12uwy+fiUoUWxXqK2Qk6UwoGc7sD0dF3efzodFoqK2tvSD2\nv0OhEMePH6e0tJTq6uqEw96RSIQ777wTl8vFwYMHV0TPc0mSVn0dusiG07OcS9SgYmRkJJZhe+7q\nO3rj+AMKr7x9fvlVXo6WP/3jYv57sx2Dfmafu6PjFH6/P+2mF2azmcrKSior4Y/2qvz2iIdnXwoT\nUZK/uU3a9IjruSgKvHPcTX6ejy2bc3HIWnwkbgF6NpvWmQhPh/CM+uj3Lh7+txbkEEgiEbC2XMt0\nCt/p2Zj1atprw89FyAryIuP1hyS6+mU2rlHxK0Y0kuDKuvCchQXR/eGcnBzcbjcVFRUUFRXhcrlo\naWmZc6W+UpiamqK1tTVpAxeXy8WNN97I3r17uf/++5d1z7+0tJSRkRHKy8sZGRlJejFw0SBAZEvM\nLn7ina1G7Rbz8vK47LLLYolm0b3vc2/eF9/0EArPDtM31ln40q3VFNlnVjder5e2tjYqKiqoq6vL\n6MxZr9Nw3R8VcNVOhUee9nK8M3Ex1kiC7h5vBkZ3huICDUdemGmebrFoWVNlIc9qIqQacHg18xqS\nSJIg3yKw6BU0yKiywtioyoQrvpl4gU3HhDfJ1bQkA7NXnFqNIMcoyDXN/K+iwpBTS2iRUH2eWc1I\nbXiUfJNM91B8r1WFREe/YG1ZkKb1Erac+fcXvV4vra2ts9pxRjOjz12prxRRHx0dpb+/n23btiW1\neu7o6ODmm2/mK1/5Ch//+MeXfeX7kY98hJ/+9Kfceeed/PSnP+WjH/3oso5n+cmWmGV5j+HhYXp7\ne9m8eTOFhYWx1beqqmg0mjlv3sNnhdI1EvzJh4v59EdL0Gqk2Ip+fHycxsZGcnMTcwVLheICLV/8\njI03W4P8/Bkfrqn4Z6r5pmnGpjM3szUaJMYnzpSt+f0K7Z1eYGbiYDJqWFNlwWozIWl0qIpMKBDB\n5Q4xNhFiWD4jMnveV8nEYPw3cP3mfBzBxB/Ca4oVKmxhlPAESsiNxaBSUphDaZEVq9U669pQRYQx\nt4bTDg2nHVqcvvNXbW5fwkOIG40UndQk9jmnpgVN1fP/7iMjI/T399PU1DRnLfTZmdyw/KIuhKC7\nuxufz8fOnTvj9k0/m8OHD/P3f//3PPjgg+zYsSMDo1yYT3/60xw5coTJyUmqqqq45557uPPOO/nk\nJz/JT37yE2pqajhw4MCSj2tFsYoS26T5Ervm4aL6VmRZnnffJBwO8+KLL1JUVERDQwM6nW5W5vl8\n+06DIyE+d1cXAHabji/dWkXT5hmhDgaDtLa2YrVaWb9+/bKG3wJBlR/9cop3O+JblZuVMQYy2Eml\nfp2B462pF7bXrs3Dp+YmVNq354pKXNPx/haCTVVwRSNUF8/+f6J9rp1OJ16vF5PJFKsvzs3NnXW9\n+IIw6NAyMKll2KXBIIVwBzInYDZzhFODid++n96nsrHy/L+rqkpXVxfBYJDGxsakxDB6nKiou1yu\njIp6tOQtNzc3qbIvIQQ//vGP+fWvf82BAwcuiKz7FciShCwkSXoOKFqKc83DpBDivy3FiVa1iCuK\nMmcZ2eTkJB0dHQCx2u+ogC+WNPLTX47yy2cm2bU1lztuqiLfOvNwGx0dja3oV4oJg6oKnvz9NL/9\nw8IZ52a9ylD/BJmKTlWU6Bkc9KHE4QC3EBoNbGwowZFAN651a83obYvf6xqNoGktXNEAxXE03BJC\nEAgEYuLk8/mwWCwUFBRgt9vJyclBkiRkWaa1rZ2piI1+37q0tTE9FzkUwu1L7PlZVyX41NXn/ybh\ncJgTJ05gt9tZu3ZtWkPJmRL1qOVrTU1NUuIbDof50pe+RCgU4t///d/ndGnLEherO+MuA2TD6Wcx\nk2jWQSAQYOfOnbS3txOJRGIr5sUEXFEFL77h4aZPlvGxawuRJIlIJEJ7ezuSJLFr1645OyQtFxqN\nxMf/KJc1ZTr2P+k9bx8/SpFVJlN9VKSZWpCUBRxgU52FiQTbaVZVWxlbYKtfrxPs2ADvq4f8BJwz\nJUnCYrFgsVioqqpCCIHf7491zpqensZoNDI9PU1VVRVb11byPjXMW906jvVqk2pIMh95JoVeR2LH\n02kF1+48/zeJdvPauHFjzGs8nWQi/B6t/kjW8nVycpIbb7yRa665hr/927+9IExrsqwesivx91bi\nHo+H1tZWqqqqYsYMLS0taLVaysrKztvjnIvTIyECQYW62plEGafTSWdn5wVheHF6VOa7P3Mz6T5/\n/9MouxkcSa0t63zUrzNyfJFGKvGQlyuRX1pGMIGcPb0eGi6pIhg+/3c1GwW7N8Flm2Z6maebkZER\nenp6KCkpwe/34/f7yc3NxW63IxmLeO1UHqPu9IhFrj5M32hi77m6SeXqrbP/NjQ0xODgIE1NTctW\nSpXISj1q4DI2NsbWrVuTWsW3tbXx2c9+lrvvvjubLJYesivxNLOqRVxVVUKhED09PTgcDrZs2UJO\nTk4seS0cDjM5OYnL5cLr9WKxWLDb7RQWFmI2m+cV9agZzNTUFI2NjRdE6E1VVY63dvPL540MTpwZ\nb7FVpa11IiPnzM/T4PeG8AdSX+ZfuruC3uHELs9Ltubj15y/MquvFvx/u2c6qKUbVVXp7OwkFArN\n2ksWQuD1emN76oFAkGntOno9VchzGK/Ei1ZScXsihCLxPzsLcgWf+7BApz0z5o6ODmRZpqGhIe1e\n4Kkwn6hHW4hqNBrq6+uTWj0/99xz/OM//iMPP/wwW7duXfwNWeIhK+JpZlWLuM/n4+jRoxQVFVFb\nW4skSfPufQshmJ6exul0vveQDcRWAHa7PTbL9/l8tLW1UVpaypo1a5a99CQepqenaW1tpbS0lMrK\nap74r2kOvjqTKV6ZH+RYS+or5blYX6WlvSt1q7PGhgLGvIkr7lV7Kxg/q1uZySD477tg67qUhzQn\n0VLFkpKSRa+NqB/3yLiHY4N2nKHkQtfJJLR96mqVuqrEx7wSUFUVh8NBe3s7Go0m1pEskfC7qqp8\n//vf57nnnuPAgQPZmuv0srIvoAuQVS3iwWCQqakp8vPz5zVumY+zVwBOpxNFUdBqtQSDQbZs2TLL\n93ylIoRgZGSEgYEBGhoaZu0Xvng0wKO/8+IZncQ7nf4N8aICGBlO3f3NoJdYu6kCpyex8jd7gY6S\ntWWI9/ae15cLPvI+sGYoShzdl62vr0/q2ugdgxfadEyHEktjMRBmOIHWthsrBZ/eN3Obu91uTp48\nmbQZynLg9XppaWmhrq6OwsLChBPlQqEQd9xxB1qtlh/+8IcZL3n79re/zf79+5EkiaamJh588MEL\nInKXAlkRTzOrWsSFEIRCobhKxxYiFArF9s/NZjMejwdJkmKr9Pz8/BWXDBNNuNNoNGzatGnOEqGe\n00Huvq8Xhyv9XqDpKinbcUkxA5OJ52desaeQyaAFvU5wzQ7YVZfyUOZECEFPTw9ut5umpqaUrEgj\nMvy+RU/3aHzhbJNOZWg8EpuoLIZWI7jtwwJbrmBwcJCRkRG2bt16wYjK2NgYvb2989asw9zh92Aw\nSGdnJ7t27eIrX/kKH/vYx7jjjjsyfs8ODQ1x5ZVX0tbWhtls5pOf/CQf+tCHuPHGGzN63mUmK+Jp\nZlVnp4+Pj6MoCnl5efMat8RzjO7u7tjMP0o4HMblcjE6OkpHRwcGg4HCwsI5a4aXGrfbTXt7+6IJ\nd+uqTXznHzbw9fsHaOtKX1c0rQZ6+9N0PJ0RSDxSIGvNrCkWfPRysGeoR0c4HKalpQWr1cqOHTtS\n/s31Orh2e4S3u1Xe6NIhFnkeqmEvQpjjPv6mKrBaFNra2gHYuXPnitr/no/oRGlqaoqdO3cuWAEy\nV/Z7V1cXv/rVr/j2t7+NXq+no6ODJ554gmuvvTbjEQhZlgkEAuj1evx+PxUVFRk9X5aLj1Ut4m+/\n/Tb33HMPGo2GvXv30tzczO7du+MKoUX7iCuKMmfpmMFgoLS0lNLSUoBYzXBfXx8+n4+cnJxZSXJL\ngRCC3t5enE4n27Zti+u8dpuer//dOn706DDPHnGmZRzrqo20taceSi8tMXF6LHEB31BrYVcdXN7A\nnH7g6SBairVhwwaKi4sXf0MC7FyvUJgnOHRcT3gBK1dvMLFVf31ViLffPkZ5eTlVVVUrfv8bZu7D\n1tZWLBYL27dvT3jMkiTR2dnJ0aNHefbZZ9mwYQNvvfUWR44cYWBgIKMiXllZyZe+9CXWrFmD2Wzm\nmmuu4ZprrsnY+bJcnKzqcDrMCJvD4eD3v/89hw8f5rXXXqOsrIx9+/bR3NxMY2PjeauR6Ep2zZo1\nlJeXJ+X85PP5YvvpwWCQ/Pz8WPg9E92fom5xNpuN2trapEKFzx5x8qNHh5Hl1C6D9ZU62k+l7jFa\n35DDhDexut+aCj23fdpOdXlm6vWjZU2jo6M0NTVldILm8kk8e1SP23/+b5lnVOgdjn+CYzEqXF7x\nGg0Nye3ZLweBQIDjx4/H7sNEUVWV++67jxdeeIHHH388I3XvC+Fyufj4xz/OE088gc1m40/+5E/4\nxCc+wZ/92Z8t6TiWmJU/M7zAWPUifi7R1eqhQ4c4dOgQbW1t1NfX09zczBVXXMGPfvQjtm/fzic+\n8Ym0PaCj+3QOhwOn04mqqjFnr4KCgpRDmtGQfzrc4tq6pvn6/QM43cntk1tzNbidgZTNXSQJNjZW\nxp3QJknwx815fOIaKzpdZp4jsizT1taGXq9n06ZNS5IHEYrAwXf1DEzOvkby9GF6E6gNr8rp58qG\nAMXFxSsyh+NcnE4nHR0dNDQ0kJ+fn/D7A4EAn//858nPz+df//Vfl6Vt6i9+8Quee+45fvKTnwDw\n8MMP89prr/GDH/xgyceyhGRFPM1kRXwRFEXh+PHjPPbYYzzwwANs2LCBxsZG3v/+93P11VdTUFCQ\n9rCjLMu43W4cDgdutxutVhtbpVut1rgfsIqi0NnZSTgcpqGhIW1ucQ5XhH/+fj/t3YHFX3wODeuN\nvJuGkrXNm2xM+uObRNnz4S8+aaNpU+aazfh8PlpbW5NeFaaCEPBqp45jvTO7Y8nUht/0wQB64cbp\ndOLxeNDr9bGJZCLX3FIQjXQka+AyOjrKZz7zGT71qU/x+c9/ftm2DV5//XVuuukm3nzzTcxmMzfe\neCO7du3iC1/4wrKMZ4nIiniayYp4HDz99NPcfffd/PjHP2bLli288sorHDx4kCNHjqAoCldddRXN\nzc3s2bMnI+HTcDgcC717PB5MJlMsSS7qwX0uUVGZ6SlemfYHVURW+cHDw/zXC66E3ldig6GR1PfD\nd7+vku7BxVfh79um44OXBZj2OYlEIthstliEI12Tmmgnry1btixpV7pz6RzWcKRFT65RTqg2vKJQ\ncMt/m/36YDCIy+XC5XIxNTWFwWCIfW/RRNClJmo6oygK9fX1SUWo3nnnHW677Ta++c1vroj953/4\nh3/giSeeQKfTcckll7B///4V1XM9A2RFPM1kRTwORkdHsVqt51lNCiFwu90cOXKEgwcP8uqrr1JQ\nUEBzczPNzc1s27YtI9m9UQ9up9PJ9PQ0ubm5MVE3Go0MDg4yPDy8JK1On/m9g588MUowtLigVpbq\n6etLvSe5xaLFVlZKODL/5WjN0XDznxRw6ZYzkypFUfB4PLHyIiEEBQUFsX8S/a2iohKJRGKd7pab\nCY/Ef74NPSPxPyv/+6Uqly5SYjdfh7aoqGd6NRttulJUVJSU6YwQgieffJL77ruPxx57jE2bNmVo\npFkWISviaSYr4mlEiJn62oMHD3L48GHeffdd6urqYkly69atS/vDLmrX6XQ6mZycxOv1YjQaqa2t\npaioaEkarkw6I/z7YyO89ObCYfL6WgPH21KvDd+5s5j+8fkF85J6E7d+soD8vIVFWZbl2GrT5XKh\n0Wjiru0PBAK0tLRQWlpKdXX1isrkng7Cr16S6BtbfExajeCL14mE/OGjHdqioj5fh7Z04fV6aW1t\nZcOGDUkln6mqyr333stbb73FY489tmK6CK5SVs6NcpGQFfEMoqoqra2tMVE/ffo0O3fuZN++fezb\nt4+ioqK0PeyiiT7r1q1Dr9eft9q02+3YbLaM1v0ea/Pxw0eG52yWotOCVkTwpcH9bfuuKgbnKC0r\nLtDy8Wut7N2VQLuxs4jW9ke3LQwGw6x94ehvNTk5SVdXV9Lua0uBqsKhYxKvnVz4+mpYI/jEVand\n1tEObdHvbnp6mpycnNh3Z7FYkr7Ox8fH6enpWdDAZSH8fj9/+Zd/SUVFBffdd9+KiJascrIinmay\nIr6EhMNhXnvtNQ4dOsTvf/97QqEQV1xxBc3NzVx++eVJPaSizVa8Xi8NDQ3nuWtFV5tOpxO3241O\np5uVJJf+pDzBr/9rksefGicQPBNir1trpPVk6glt5WVmIvrZwllcoOVjf2Tlql0WdNr0fZ5gMBib\nDE1NTWE2m1EUBUVR2LZt2wWxd9nSB0+9JiErc38vn96nsrEyvec8u8+Ay+WKdWiLivpCzYPOPkZv\nb2/M6S6ZiNLw8DB/9md/xp//+Z9z6623rqhoySom+yOkmayILyNTU1P84Q9/4ODBg7z88svk5ubG\nQu87duxYdNXg9/tpbW2lqKiItWvXxvWQCoVCsf30qDBF99NTWTGdy6Qrwv7HRnjxjRnhrq3Q0tmd\nerOTPXvKOTU08+9FBVo+9oE89l6ak1bxnotQKMTx48fR6XRotdrYajM6IYpHmJaD8fFx3j05Spuz\nCY9/dhQm1yy442OCTOeozeWLkJeXF9tTPzcZVFEUWlpaMJvNbNy4Manv9c033+QLX/gC3/3ud2lu\nbk7XR8mSOivvJrnAyYr4CiHajCRan/7OO+9QW1sbE/WNGzfO2qMdHh5mYGCA+vr6pOpko+c8O0nO\n7/fHHq52uz0tntnH2nw8+uQoLS0u1MR6lJyHRoJ1DZXoNBIf/aM8rl4C8YYzjUA2btwY25ONCpPL\n5cLhcBAMBmc11lhuv3EhRCxCs2XLFmRVz5OvSJwaPvN9va9e8MEdS39LCyGYmpqKRYhCoVDsuzOb\nzXR2dlJVVZWUBakQggMHDnD//ffz+OOPs2HDhgx8giwpkBXxNJMV8RVKNPM5up/e09PD9u3b2bNn\nD0899RTNzc3cdtttad3jiz5co6KerpIsVRWcaJvg8Au9jDssdPVGEu6MppFg53Y777+6dEa8M2TY\ncjZR97WxsTG2bNmyYPlgtHXoud9dNIS8FAmGUSKRCCdOnMBqtbJ+/frYfRUsDAAAGZdJREFUSlYI\nOHJc4sUWAInPfVilOLn5X1qJmh0NDw8zOjqK0WiMXXOJOBgqisLXvvY12tra+NnPfpb05DZLRsmK\neJrJivgFQiQS4eGHH+arX/0qGzZswOfzcfnll9Pc3MyVV15JXl76u3hES7IcDgculwtJkmYlycVT\nKxzN2B8ZGaGxsZGcnBxUVdA7EODd1inebfPSctIbE3WzSUNVhYnqChNVFWbWVJioqjBRVW7CYFi6\n2uSo+5rBYKCuri7humhVVXG73bMSDKMTIpvNlrEEq2gm97p16+btg91xGt7olPjMB1bO7Rwti9y6\ndSsGg2FWKaAsy7EJUUFBwZyi7vP5uPXWW9mwYQP33ntvxhPY3G43t9xyCy0tLUiSxAMPPMD73ve+\njJ7zIiEr4mkmK+IXCC+//DJ33nknDz30EOvXr8fn8/HCCy9w8OBBXnzxRUwmUyzrfdeuXRmxkYxE\nIrOS5KIGIHa7fc5a4UgkMksI58uMV1XBwFCQ3BwtRfalt788F5/PR0tLCzU1NWlzX4u68EW/u2ir\n2oKCgrgnRIsRNZ2JJ5NbVcn4Xng8qKpKZ2dnrNZ+rmvk3Pp+VVWx2Wz4fD5qamoIBAJ85jOf4XOf\n+xw33njjkuQm3HDDDVx11VXccssthMNh/H7/iq1UWGFkRTzNZEX8AkGWZYQQc4ZlhRCMj4/H9tPf\neustqqur2bdvH+9///vZvHlzRhy2otnbUQMQi8USS5ILh8O0t7dTW1sb6+R2ITAyMsLAwEDGjXKi\n5Wwulwu3241er581IUrk94q20wwGgzQ2Nl4wZVRRA5fCwkJqamriFl9FUXC73Tz00EP8/Oc/Z2Ji\ngmuuuYbrr7+eK6+8MuMGRx6Ph+3bt9PT07MikxlXONkvLM1kRfwiRFVVTp06FdtP7+zsZOvWrTFR\nT6bz2mJEy4ocDgdDQ0MEAgGKioooKSmJOcmtZBRFoaOjA1mWl8V9LWpzenbVQHSlvlD/+agQ2u32\nuCsUVgLRaMf69euTatUqhOBnP/sZP/nJT9i/fz8DAwM8//zzvPnmmxw+fDijv9+xY8e49dZbaWho\n4N1332Xnzp1897vfTapEdBVyYVygFxBZEV8FyLLM0aNHY6LucrnYs2cPzc3NXHXVVWmrF49EIrS2\ntmI2m2Mh/+hKXVGUWUlyK2m1GAgEOHHiBGVlZSvCfS3qiHa2te5c5WzRnuVnZ81fCExMTNDd3Z20\n17wsy9x999309vbyyCOPLLlf/VtvvcWePXt4+eWX2b17N7fffjtWq5Wvfe1rSzqOC5SsiKeZrIiv\nQvx+Py+99BIHDx7khRdeQKvVsnfvXpqbm7nsssuSWjVHe6zPl1AVDYFG9zWje8LxWJxmkomJCU6d\nOpV0S8ul4GzzFKfTSSAQQKvVEgqF2LJlywVjIyqEoK+vD5fLlbSBy9TUFDfffDPbtm3ja1/7WkYd\nCOdjdHSUPXv20NfXB8CLL77Ivffey+9+97slH8sFSFbE00xWxFc5QggcDgeHDx/m8OHDvP7665SV\nlcVC742NjQsKrBCC/v5+JiYmFi3DOpu5LE6j++kLhY/TRbSOempqii1btixLP+lkUFWV9vZ2gsEg\nNpsNl8tFJBIhPz8/FuVYiZ9FURRaW1sxGo3neR7ES29vL9dffz1/9Vd/xf/8n/9zWSMmV111Ffv3\n72fTpk3cfffdTE9P881vfnPZxnMBkRXxNJMV8bN47rnnuP3221EUhVtuuYU777xzuYe05Agh6Onp\niSXJnTx5koaGhlhntrPDzdPT03R2dpKTk8OGDRtSWk2fHT72+Xyx8HFhYWHa27tG95FtNltGmtJk\nimAwyIkTJygpKZnVyUtV1Vj2ttPpRFXVWd3ZlnvrIhgMcvz48Vhb3GR48cUX+Zu/+Rv+7d/+jT17\n9qR5hIlz7NixWGb6unXrePDBBy+YiMgyc2HcbBcQWRF/D0VRqKur4+DBg1RVVXHppZfy2GOP0dDQ\nsNxDW1YUReHdd9+N7aePj49z2WWXUVFRwWOPPcavf/1rampq0nrOuWw6oyvNRMw/5sLlctHe3k5d\nXR2FhYVpHHVmiY5706ZN2O32BV87VzlbtL4/Pz9/SUPQUbe7ZJvFCCF46KGHePTRRzlw4ADV1dUZ\nGGWWJSQr4mkmK+Lv8eqrr3L33Xfzn//5nwB8/etfB+DLX/7ycg5rxeH3+/nCF77A4cOHqampIRgM\nxvbT9+zZkxG70aijl8PhmLXSjIaP4xElIQQDAwOMj4/T1NS07Lao8RI1yxkdHU163OfW96dSzpYI\nQ0NDDA0NsXXr1qTGLcsyX/nKVxgbG+Ohhx7KZn9fHGRFPM2snBThZWZoaGjWLL+qqorXX399GUe0\nMrnnnnsoLS3l1KlTaLVaXC4XR44c4be//S133XUXhYWFMb/3rVu3pmXVp9FosNls2Gw21q9fH1tp\nOhwOuru70Wq1szqznStKsizH9mN37ty5bEl0iaIoCu3t7QDs2LEj6e9Sr9dTUlISSziMNsEZHBxk\namoKk8kU+/7SkY8QrVsPhULs3LkzqXG73W7+/M//nD179vCv//qvF8xvliXLUpMV8SwJ8U//9E+z\nsortdjvXXXcd1113XWy1e+jQIe6//36OHz/Opk2bYqJeW1ublv1nnU5HUVFRrKwqHA7jdDoZHh7m\n5MmTmEymWJKcqqq0tbWxdu1aysrKUj73UhEteysvL6eqqiqt+/ZGo5Hy8vKYG100H6Gvr29WPkIy\n3dmivu0FBQXU1dUlNe6uri5uuukm/vZv/5ZPfvKTF0zOQpYsy0E2nP4e2XB6+lFVlZaWlth++uDg\nILt27aK5uZmrr76awsLCjDygo53ZhoaG8Pl82O12SktL09aZLdM4nU46OjqS3kdOhbnK2eLtbBc1\ncFnIt30xnn/+eb785S/zwAMPsGvXrmQ/RpaVS3ZGlmayIv4esixTV1fH4cOHqays5NJLL+XnP/85\njY2Nyz20i4ZwOMyrr77KoUOHeP755wmFQlx55ZU0Nzdz+eWXY7FY0nKeqPuaoijU19fParcaDodn\nJcktZXexxYiW601OTtLU1LQiXO7ObRt69vd3djlbqgYuQgj279/PL37xCw4cOJBUG9IsFwRZEU8z\nWRE/i2eeeYY77rgDRVG46aabuOuuu5Z7SBc1Ho+HP/zhDxw8eJBXXnmFvLy8WOj9kksuSao0yu/3\n09LSMm8Yeq7uYmd3ZlsO8xA4U0edbNe0peLscjaXy4WiKGg0GmRZZtu2bUlNxCKRCH/zN3/D9PQ0\n+/fvT3tJYZYVRVbE00xWxFcYp0+f5vrrr2dsbAxJkrj11lu5/fbbl3tYGUcIwfDwcKw+/Z133mH9\n+vUxUY+nDj26Gqyvr4/bfU2W5VmZ2zqdblaS3FLsx/r9fk6cOEF1dfUFtQJVFIWWlhaEEFgslqTK\n2ZxOJzfccAMf+MAHuPPOO1fs5CVL2siKeJrJivgKY2RkhJGREXbs2IHX62Xnzp38+te/XnX16lFn\nsuh+em9vL5dccklM1EtKSmICqygKPT09+Hw+GhsbU6ojj2ZuRxuRWCyWmKhbLJa0i/rk5CRdXV00\nNjZitVrTeuxMEjVwqaiooKqqKvb3ucrZoqJ+buXAyZMnueWWW/jqV7/K//gf/2PJEtgURWHXrl1U\nVlby9NNPL8k5s8TIiniayYr4CuejH/0on//85/ngBz+43ENZViKRCG+88QaHDh3i97//PT6fj8sv\nv5zt27fzgx/8gHvuuYfm5ua0CoEQYtZ+ut/vjzvJK55j9/b2xnzEV6JV6nxEG69s3rx5UZey6KTI\n5XIxNTXF22+/zeTkJOXl5TzwwAM8/PDDbN++fYlGPsN9993HW2+9xdTUVFbEl56siKeZrIivYPr6\n+ti7dy8tLS0X1CptKfB6vfzwhz/kW9/6Fps2bUKSJK6++mr27dvHrl27MpKwFk3yiop6JBKZ1Zkt\n3nPKskxLSwsWiyVlu9qlZnh4mMHBQZqampLauz516hTf+ta3eOmllzCZTGzZsoX3v//9fPrTn16S\nBjSDg4PccMMN3HXXXdx3331ZEV96siKeZrJ14isUn8/Hxz/+cb7zne9kBXwOjhw5wu9+9zveeecd\nKioqGBsb49ChQzzyyCPccccdrFmzJub3vmnTprQIpSRJ5Ofnk5+fT21tLYqi4PF4cDgc9PX1zdoP\nttlsc54zWoZ1odWtCyHo6uoiEAgkbeASCoX49re/jSRJnDx5EoPBQHt7O4cPH0aW5QyM+nzuuOMO\nvvGNb+D1etN63P/zf/4PdrudO+64A4C77rqLkpKSVZHPkmV5ya7EVyCRSIQPf/jDXHvttXzxi19c\n7uGsSHw+H0ajcc7Vb9QxLLqf3tXVxbZt22Kd2crKyjKy/3rufrDBYJhlbzoxMUFPTw+NjY3k5eWl\n/fyZIhKJxKJByTaMmZiY4IYbbuDDH/4wX/ziF5cl+vD000/zzDPP8IMf/IAjR47wrW99K20r8b6+\nPq677jqOHj2Kqqps3LiRN95444Ly518isivxNJMV8RWGEIIbbrgBu93Od77zneUezkWBLMu8/fbb\nMVH3eDzs2bOH5uZmrrrqKvLy8jIi6sFgEKfTicPhwOFwIEkSa9eupbi4OGEntOVienqaEydOpGTg\n0traymc/+1m+9rWv8cd//MdpHmH8fPnLX+aRRx5Bp9MRDAaZmpriuuuu49FHH03L8T/4wQ/yjW98\ng7GxMfbv388vf/nLtBz3ImPlX/QXGFkRX2G89NJLXHXVVTQ1NcVWK//8z//Mhz70oWUe2cXD9PQ0\nL730EgcPHuSFF15Ar9fHmrhcdtllaU0yi9qQ5uXlUV5ePssJzWq1xlbqK8HY5VwmJyc5depUSpGD\nZ555hn/6p3/i0UcfZcuWLWkeYfKkeyUO8MQTT/DKK68wOjrKDTfckL1n5yYr4mkmK+JZVjVCCCYn\nJzl8+DCHDx/mjTfeoLy8PBZ6b2hoSDr06/V6aW1tnXMVG+3MFhV1RVFmJcktZw/wqAd+1DkumUmN\nqqp897vf5fDhwzzxxBMUFxdnYKTJkwkRD4fDNDU1EYlE6OrqWjbjoBVOVsTTTFbEs2Q5CyEE3d3d\nHDp0iMOHD3Py5EkaGxtjSXLxNiMZGRmhv7+fpqamuFpoKooyy0lOkqTYKj0/P3/J9pAVReHkyZNo\ntdqkEwKDwSD/+3//b8xmM/fff/8FVT6XKn/5l3+JzWbj3nvvXe6hrFSyIp5msiKeZV6yphgz38Gx\nY8di++kTExPs3r2bffv2sXfvXmw22yxRjybVBYNBGhsbk15Rh8PhWJKcx+PBYDD8v/buP6aq+o/j\n+PNOqWwYAl+hpWimjhQkgkiwQJEh/MFwueVWqbQy+2HNrX+qaTNlU5pzSPZHba2mE75ka9M2m+1e\ncKZcZOGSYDWmS77C7UYOuQpc8Ar3fP/4zruY5hev53Luhdfjv8vGve+zoa/7Oe/P+bwDk9nMGBd6\nO9evX+eXX37h4YcfHjWW9250d3ezYcMGnn/+ed55552I6Pubxe/3k5GRwTfffMPChQutLidcTZ4/\niHGiEJd/pEMxbjU0NERDQwN2u52TJ09iGAa5ubmsXLmSpKQktm3bxs6dO5k/f76pAXZzXOiVK1dG\njQuNj4835azxmwe4JCcnExcXF9R7tLS08MYbb/Dxxx9TXFx8zzVFkl9//ZWSkhKee+459u7da3U5\n4UwhbjKFuNyWDsX4/wzDoLe3lxMnTlBTU0N9fT1PP/10YJPckiVLQtIXNQyD/v7+QKgPDQ0RExND\nfHz8qMliY+V2u7l06RJpaWlBfSEwDIPvvvuOPXv2UF1dzaJFi+76PWTSUIibTIe9yG2F6lCMieRm\n33pwcBCXy0VzczNTpkzB4XCwf/9+WltbSU5ODvTTH330UVNW5zabjenTpzN9+nTmzp0b2CTX09PD\npUuX8Pv9gUNnYmNj//GLhGEYXLhwAa/XS2ZmZlC3/v1+P3v27MHpdOJwOIJexYtIcLQSl1uE8lCM\niejMmTOkpaXdMobT7/fT2toa6Ke7XC6ysrLIz88nLy+P+Pj4kPSMh4eH8Xg89PT04PF4mDJlyqjJ\nbDdHh7a2tt7TAS5er5e33nqLmTNnsm/fvrCazS5hSytxkynE5RahPhRjsrp+/TqNjY04HA5OnDiB\nz+cjNzeX/Px8cnJygprFPRY+ny9w6/3q1atERUXh9XqZO3cuc+bMCSrA3W4369evZ926dbz55puT\nagOb3BP9oZhMIS53pJV46Hg8Hk6ePIndbsfpdBITExMYtZqenh6SZ8V7enpob28nISEBr9fLwMAA\n0dHRgZ3vY5nMdvbsWTZv3kxlZSUFBQWm1/h3nZ2dbNiwge7ubmw2G5s2bdJ55JFNIW4yhbjckUJ8\nfBiGgcvlCjyf/vPPP7NgwYJAqM+fP/+enhU3DIPOzk7++usv0tLSApvfDMOgr68vsFL3+XzExMQE\nbr///Ra5YRh8++23VFVVUVtbOy6PUbndbtxuNxkZGfT19ZGZmcmRI0dYvHhxyD9bQkIhbjKFuEgY\n8vv9/Pbbb4F+ekdHBxkZGaxYsYIVK1aQkJAw5lvYN9/LZrPx+OOP3/HLgN/vH3XojGEYfP/996Sn\np9PS0kJrays1NTXMmDHDrEu9K6tXr+btt9+msLDQks+Xe6YQN5lCXMKax+Nh48aNtLW1YbPZ+PLL\nL8nJybG6rHF348YNmpqacDgc1NfX4/V6WbZsGfn5+TzzzDNER0ff9vduHuCSmJhIUlLSXfeuh4eH\nqamp4eDBg4EJbIWFhaxatYqMjAwzLm3MOjo6yMvLC0xUk4ikEDeZQlzCWllZGbm5uWzcuBGfz4fX\n67VsFRhOrl27xo8//ojdbqehoYEHH3wwsErPzMwkKiqKxsZGBgcHeeKJJ4IeidnV1cX69et57bXX\nePXVV3G73dTX19PV1cX7779v8lX9s/7+fpYvX87WrVtZs2bNuH2umE4hbjKFuIStq1evkp6ezu+/\n/67dz3dgGAbd3d04HA4cDgdnz54lOjqay5cvs3fvXgoKCoLqpzc1NbFlyxb279/P8uXLQ1D52Ny4\ncYOSkhKKiop49913LatDTKF/yCZTiEvYOnfuHJs2bWLx4sW0tLSQmZlJVVXVmAaKTFZ+v58PP/yQ\npqYmioqKaGho4MKFC6SnpwcmsyUmJt7xS5FhGNTW1vLZZ59x+PBh5s2bN45XcGstZWVlxMXFsW/f\nPsvqENMoxE2mEJew1dzcTHZ2Ng0NDSxdupQtW7bw0EMPUV5ebnVpYcvpdHLs2DHKy8sDq+/h4WGa\nm5sDm+SuXbtGTk4O+fn5PPvss6P6yyMjI+zcuZP29naqq6uDniNultOnT5Obm8uSJUsC17Nr1y7N\n6o5cCnGTKcQlbP35559kZ2fT0dEBwKlTp6ioqODYsWPWFhbh+vv7OX36NHa7nVOnTnHfffeRl5dH\ndnY2n3/+OampqezatUvzsCUUFOIm09npErZujsRsb28nOTmZuro6PR9sgujoaIqLiykuLsYwDC5f\nvkxdXR2VlZUsXbqU3bt3aw+CSITQSlzC2rlz5wI70x977DG++uorYmNjrS5LRIKjb4cmU4iLiMh4\nUYibLPhzHEUmmcrKSlJSUkhNTeWFF15gaGjI6pJEZJJTiEtQfvrpJ9LS0hgaGmJgYICUlBTa2tqs\nLitkXC4Xn3zyCc3NzbS1tTEyMkJtba3VZYnIJKeNbRKUrKwsSktL2bZtG4ODg6xbt47U1FSrywqp\n4eFhBgcHA6M8H3nkEatLEpFJTj1xCZrP5yMrK4sHHngAp9M54R9JqqqqYuvWrUybNo1Vq1ZRXV1t\ndUkikUY9cZPpdroEraenh/7+fvr6+iZ8f7i3t5ejR49y8eJF/vjjDwYGBjh06JDVZYnIJKcQl6C9\n/vrrlJeX89JLL/Hee+9ZXU5IORwO5s2bx8yZM4mKimLNmjU4nU6rywpbx48fJzk5mQULFlBRUWF1\nOSITlnriEpSDBw8SFRXFiy++yMjICMuWLaO+vp6VK1daXVpIzJkzhzNnzuD1epk2bRp1dXU89dRT\nVpcVlkZGRti8eTN2u53Zs2cH9k/ooB4R86knLjJG27dv5+uvv2bq1Kk8+eSTfPHFF9x///1WlxV2\nGhsb+eijj/jhhx8A2L17NwAffPCBlWVJeFBP3GRaiYuM0Y4dO9ixY4fVZYQ9l8tFUlJS4PXs2bNp\namqysCKRiUs9cRERkQilEBeJEK+88goJCQmjnse/cuUKhYWFLFy4kMLCQnp7ey2s8H9mzZpFZ2dn\n4HVXVxezZs2ysCKRiUshLhIhXn75ZY4fPz7qZxUVFRQUFHD+/HkKCgrCYid4VlYW58+f5+LFi/h8\nPmprayktLbW6LJEJSSEuEiHy8vKIi4sb9bOjR49SVlYGQFlZGUeOHLGitFGmTp3Kp59+SlFREYsW\nLWLt2rWkpKRYXZbIhKTd6SIRpKOjg5KSksA59TNmzMDj8QBgGAaxsbGB1yJhSLvTTaaVuMgEYbPZ\nsNn0f6TIZKIQF4lgiYmJuN1uANxuNwkJCRZXJCLjSSEuEsFKS0s5cOAAAAcOHGD16tUWVyQi4+lu\ne+IiYhGbzfZvYAXwL6Ab2A4cAQ4Dc4D/AGsNw7hiVY0iMr4U4iIiIhFKt9NFREQilEJcREQkQinE\nRUREIpRCXEREJEIpxEVERCKUQlxERCRCKcRFREQilEJcREQkQinERUREItR/AeyE6lGyI6NrAAAA\nAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fe0b1335cc0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from mpl_toolkits.mplot3d import Axes3D\n",
    "import matplotlib as mpl\n",
    "\n",
    "fig = plt.figure(figsize=(9, 6))\n",
    "ax = fig.gca(projection='3d')\n",
    "surf = ax.plot_surface(X, Y, Z, rstride=2, cstride=2, cmap=mpl.cm.coolwarm,\n",
    "        linewidth=0.5, antialiased=True)\n",
    "ax.set_xlabel('x')\n",
    "ax.set_ylabel('y')\n",
    "ax.set_zlabel('f(x, y)')\n",
    "fig.colorbar(surf, shrink=0.5, aspect=5)\n",
    "# tag: sin_plot_3d_1\n",
    "# title: Function with two parameters\n",
    "# size: 60"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "collapsed": true,
    "uuid": "5918f2cf-3ead-4b80-980e-4a375ee159db"
   },
   "outputs": [],
   "source": [
    "matrix = np.zeros((len(x), 6 + 1))\n",
    "matrix[:, 6] = np.sqrt(y)\n",
    "matrix[:, 5] = np.sin(x)\n",
    "matrix[:, 4] = y ** 2\n",
    "matrix[:, 3] = x ** 2\n",
    "matrix[:, 2] = y\n",
    "matrix[:, 1] = x\n",
    "matrix[:, 0] = 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "uuid": "48ce242e-3411-41bf-b6c1-c8e228f3e494"
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/lab466/anaconda3/lib/python3.6/site-packages/statsmodels/compat/pandas.py:56: FutureWarning: The pandas.core.datetools module is deprecated and will be removed in a future version. Please use the pandas.tseries module instead.\n",
      "  from pandas.core import datetools\n"
     ]
    }
   ],
   "source": [
    "import statsmodels.api as sm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "collapsed": true,
    "uuid": "b9eb74bd-9280-4d8b-ae7d-8853911389cb"
   },
   "outputs": [],
   "source": [
    "model = sm.OLS(fm((x, y)), matrix).fit()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "uuid": "cc9c9f77-9051-4d82-bb7b-c646216d542f"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.rsquared"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "uuid": "b68898de-9001-4a15-a5ee-7ee50c5592ea"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1.34614542e-15,  2.50000000e-01,  1.33094539e-15, -2.84494650e-16,\n",
       "        5.00000000e-02,  1.00000000e+00,  1.00000000e+00])"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = model.params\n",
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "collapsed": true,
    "uuid": "1f5d1574-8238-45e4-987d-bdb7cc6b5e03"
   },
   "outputs": [],
   "source": [
    "#def reg_func(a, (x, y)):\n",
    "def reg_func(a,*args):\n",
    "    x = args[0][0]\n",
    "    y = args[0][1]      \n",
    "    f6 = a[6] * np.sqrt(y)\n",
    "    f5 = a[5] * np.sin(x)\n",
    "    f4 = a[4] * y ** 2\n",
    "    f3 = a[3] * x ** 2\n",
    "    f2 = a[2] * y\n",
    "    f1 = a[1] * x\n",
    "    f0 = a[0] * 1\n",
    "    return (f6 + f5 + f4 + f3 +\n",
    "            f2 + f1 + f0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "collapsed": true,
    "uuid": "fd9f8eed-1b10-4ec8-8a15-bedae7f53a18"
   },
   "outputs": [],
   "source": [
    "RZ = reg_func(a, (X, Y))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "uuid": "096451ce-173a-43b5-b81f-9dac26df2702"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.colorbar.Colorbar at 0x7fe09cf1db00>"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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sfnDMnAk355jKh/0be5r57eZS3IrKuq5SNjSN7squiEjhn7OOY1f0fIz40Kky\nfyt7mgxP15i7FjFyL0dayzjSWgbNYNOa2B85i33mTN6N71sUvrbmO5i8bgoagg9GHAn/PvnmpSfy\nJqdS1mzjr+sLQtonVxRl3Ftc02WLRHBwEX3sJgH/vrfb7R5X4Fq4aWtrY/v27Wi1WtauXTuigEP4\na51PBJ/PR1FREcXFxeTn55OdnT2uh9mmrxpRVJXLooa7tOt8Jm5qz+Oa1iX0aEw8mNvJvAgvFo3M\nRdGBXe5jUec18r4jgfUxrVwQ28HmeXu5Lr6Jd6S5XCidxQtqFj41tM+/So1iF8lcF13LOeYWHvlP\nLTe8uA+ra3gRmfEwFSLe65W5860S/vtfpcSpTiQVrmz4KOD7643xPDDvu/ws72rKozO4St6DjIbT\nOveQGYSAj0SU7GKdrYJje4pxafSc2bMHo1Hib6dew/+edAUd5ontZ2tQOfubLRxf9BnFrU4uePRL\nPikfv0cmlBzx3t5eIiMPrS0XwdgISzyM+FPGent7KS4upqCgYErE239+SZJYuXIlJtPolsBkWOLj\n7fEN0NLSQnl5eUhV4qBvj/XlXQ2cFNHOLN0B69euaHnMmskztgx0EvzXHCtXZ9ho92i5pTiOK2Ma\nidKEHhPwjDUdjQTfi2sFwKxVuDm5gfNi2rm3dTYPOlbwurSQW9SdrJJaxzX2C+RgkBQujWoiTuNl\nicHGfZUL2PDETv5yUT5ZyaGVaz3Yi7aqDic3v7KfinYnV2rLeEOZy2prOWme7mHvbdNH80LaUXyU\nsASjJHO1vJdLlSL+qVmErEqc07FzwvN5PWEVkaqHa7s+w9C5jVdjlvPPzLXcOesWvrN7C6fu24Z+\nlJzx0VCB0vSFzHJ3IrlUfvTiPs5baGDDsnhivq1jEKijmx+fzzduEbfZbKJu+mGIEPEwMdB1rtFo\nJq1RyVhzqKqqoqWlhZycHBISgts/nSwRD9Yl2NvbS1FRETqdbtTAtbEWBW/sacHmVrgypaH/tW/c\nUfy0YxGtPgPnJju5eV4PKca+a326wYJGgsujQw9q6pZ1vGZP4azoDpL1g0t/zjO6eTSjjI/sMdzb\nOpsfeU/gZLWWW9hFfBAu9m7VwNvM4+zIFuK1fWNfEtVEtsHBze2LuOypXdx9dg6nL0oOae4H6/u5\neV8rv9lcglHx8DfjDlrVCLplA2e37Bj0PrvWyAtpR/Nu0gqQJC6Si7lC2U88bnrR8qo2m3XWctJH\nEP7x0KrTcakEAAAgAElEQVSP5tOYbM7v+Rqz2pdyuL5nJyfYS3g04VheX3k623NWs+HT11jUOP7y\nu8VpC2iMSeYnlW9xZFcxj8w9g1dZTLPXyY1rDXR0dATs6Ob/TAaWQQ4Wh8MhRPwwRIj4BDmYjUoG\nnnPoA7ijo4OSkhJSU1NZt27dlKSuDSSYIDxFUaitraWxsXHMRcdYlr2sqDz3RR1LjDaWGW2oKrxs\nT+X33QtJNSq8mN/K0ugDItvl1fB/zWbONLcFzB0Phk3WVHoVDVfHNweYN5wY1cOR5n082ZnKYx0Z\n7CWJ+9X/sEjqGnXs11iAGw3fG7I1sMJo5aWUXdzckcfPXytmX6Odm06ch04TvCgfDHe626fwwPsV\nvLSriaXaTu417CBZcnGJ+wTmutrItx/I8S42p/PggvNo11k4U6ngGt9eUjlQ8e7fmvlYMXBu+1cT\nnte/EpYDcK71m0GvJ8t2ftX6Njsi5vBw4vH8+bTrWFm1h4u/fIt4Z/BV4bYsPpoYuZejOwsxqDI3\nVb5Jjr2Bp9ST+Xm3mz9flM+aFMuIHd0iIiKIiopCo9GM+/Ox2WwiR/wwRIh4iIzWqGQyGSpmLpeL\n4uJiVFVl+fLlRESMv1znZIj4WGP29PRQWFhIYmIia9euHdNiH2tRsK28k9puN/+VWI9blbincyGv\nOVI5Js7FH3I7idUPPvaFRjO9isTVMaGng7kUDc/b0jnW3EOW0TXqe00alR8lNnG8pYcbGxby/7wn\nc7u6gzOl6hHf71U1vCxlc4SxiyzD8PKtyToPTyXv4YGu+Wz8AoqbbTxwXh7xZkNQc59sEa/t7OVn\n/7ef4lYnV+rK+KG+CL2k8qWcSLkSzQ3Nm5HoK9zyespanks/jlSpl3/43mWxOngPWQFe0OaR3dvM\nImfDSKcLGqfGwHvxSznWUUayPHI62+reGh6tf45XYlawae4a9s/O5eqPX2BFzf4xx2+NimdPRh4X\nNH2G4dtGLRLwndadzHc288esC7jsqV3c+Z0czlmSMqyjm8vlwmq10traitVq5csvvxzU0S0qKirg\nb0W40w9PhIiHQLijzseDRqPpz+muqamhqamJrKwskpKSJjSm35MQLgIFy/l8PkpLS3E4HBQUFAT9\n0BlNxCVJ4tkv6knXuVmst3FF6zL2uy38cLaVn8yxDUsXc8nwXKOFYyJGFshgedOeRKes45oAVvhI\nLDI5eXlOITc3zuc3zrUUqXHcxG50QwrRfEAm7aqJ30aVBxxLL6ncEV9BvsHG3bVZXPjYV9x04gLO\nKkgeM3p9skTc4fbxxGd1PPNFPUbFw5+NOzlWeyBo8HnffGLkXo7pKqRbF8lf557N19HzOFGp4Xbf\nF1gY3o3sEymDOqK4tW3rhHuGvxdXgFNj4IKer0d9n0GVubR7ByfaS7g3+QweOfEKzty9hXO+fh/N\nKKlwH+UdiQaV01uHt0bNtTfwx72P8+DC87jjX7CnwcqtpyzAoOt7fkiSREREBBEREUiSRFRUFHPm\nzMHhcGC1WvtjRlRVHdQnwGw2o9FoRC/xwxQh4uMgHAVbJopWq6Wzs5PKykqSkpKCsmLHYjL3xP2o\nqkpLSwsVFRXMnTuXvLy8sLU3LWyy81WdlYstHWxoXYEHLf+7qIOTEke2jl9viaTDq+GahNCtOuXb\nKm+LTU5WR46v1nqczsdjmaX8qTWDjV3ZlBHHveqn/fvkqgqbpBzm6Xo5yjS6yx3gXEsr2QYHv+nM\n5o5/lbDpq3p+cepClmUEbmIT7sA2WVF5/ZtmHtpaRYfTxxnaOm4wFpKiOfAZ1ClmPpFTuaj1M4rN\nGfx5wbk4tEZulb/gu0p5QIHepM0j2WfjSGvpxOaIxL+SVpHvaiTbE1yAYarPyh8aX+F/E49n87KT\nqE2cxXUfbyLSM/y75dIZ+DRnDUd2FgUsWhPrc/Lr4uf5Z8bxvLhrHYWNVjZetRy9drAh4PP50Ol0\nSJKExWIZJM6yLGO327FardTW1mK1Wrn99ttJSUnBYrFQXl7OggULgv59XXPNNbz11lskJyezb98+\nADo7O1m/fj3V1dXMnTuXl156aUaUZT4cESlmQeAXb7fbjc/n67e+D7aAu91u7HY7NTU1LF26lIUL\nF4alXOpA6z5cDLTEnU4nu3btoq2tjdWrVzNr1qxx37vRRPzp7bUYJIWX7WnEG+Hl5a0BBVxW4al6\nC4uNdlaP0AglWD5yxlPtNXFN/PBuaMGgk+AXKfU8kFZJkSaBK6TTKVT7UgB3k0ixGsfllnqC3ebO\nMzh4PuVrfp9QQktrF5dv/IZbXyukqSewmz9c39/Pq7q46LGvuOvtMjLcrWw0fsw9xl2DBBzgBd88\ntKpKr0bPr7MvIVrr4wnvO5w3ioAXSfHslpI5u+2rMYvBjDnP6CxadVFc0DPcSh4NAzI3tW/hJ+0f\nUTgrm9+feyONMcODCT/LWkmvzsiZLaPv22tRuaL+Iy6p30ZzWw+NPcODHEcLbNNqtcTExJCZmcni\nxYs54ogjeOWVV8jJycHpdHLrrbeyfPlybrvttqCu76qrruKdd94Z9Np9993HSSedRFlZGSeddBL3\n3XdfUGMJDj7CEh+DUF3nfks0HK52RVGoq6ujvr6eiIgI8vLywpoPOlmWuM/no6qqiqamJnJzcwPm\nqQdDIPd8XWcvb+9rRUXDqYm9/D67C4su8MP+ww4TNS49DyZXhiS+fp60zmKW3sMpUWNbyqNxVkwn\n84293NiQxf/znsRt6g62MYsYrY+zzeNLR9NIcI65lZMj2nnSmslTRQofFLfx3dworlidRkpCLCaT\nKaT0v5GobHfypy0VbCvvIl3Ty32GfZysbRzxvtpUHW/45mL29fKvlDWcqVTwM3kHEYy+eNykySNS\n8XBq1/A+3+NBBV5PWkO6z8pa5+i12UdCAs627WWep517Us/i3nNv4Jqtm1heWwiAgsRHi48hy9FE\ntiO4OItqcwoenYHkqOFxDD6fb1y/8cTERJKSksjPz+faa68F+hbPwXDsscdSXV096LU33niDrVu3\nAnDllVdy/PHHc//99wc9n6lmpcasWtWpKyVdjvtdVVVPPxjnEiIegKGNSsbrOvfXOZ+oiHd1dVFc\nXExCQgLr1q2jqKjooAehhYLX62XPnj2kpaWNO1o+ECOJ+Atf1aMC38+wcvM826jCrKrwj7ooMnUu\nTooMvSTqTlcUu11R/DK5Fl0YjNlFpl5enlPIzxrnc7dzLaByTWQ9EZrQPpNIjcJPYmu4wNLMg91z\neblQ4sPKCi7KNbEyUSbCZCIiIgKPx9Pvth0PXU4vj/ynhpd2NhKBjxv1JVyiq8QoBZ7vXzyL6UWL\nqjdyl+9TTlOrxzxPM5F8qJnN2e07iVRCzyAAKI5IpyQilR+3b52QRZ/vbuKh+k38NvVMHj7pSs7a\n/QFnf/0B+2dl0xyVwCUVbwQ1Tqshmi9js7lqxSwiRijNGkqxF6fTOSg6fSIL/ZaWFtLS0gBITU2l\npSX0YkhTgU1SeMgyb8rOf4atOPFgnUuI+BDG2+M7EH4RD7WjkMfjoaSkBLfbzZIlSzCb+4p6TFYk\nebj2SL1eL6WlpdhsNvLy8khNTQ3LuCNdt93l44UddZyR6ORn88fel97ebWSvzcCvEyomJL6P92QQ\np/NxQWx76IMMIU7n4x+ZpayvzqPIbeZLdyztsp5E7fBAr2BJ07n5Q2IJG9xN3N+1gL/vVkgy68hP\n05BpcZGAC5t7NxFaBYvFQkxMzKBAKejb665od7K3wcreRhvf1HdT0e4CVC7QVXO9vph4KbDAelWJ\n//Hk8bo8FxNenvH+m0yCiyF4QZMLKpzTMT7390i8lrQKi+rhVHvhhMdKku38sfEVHko4nreWnUxt\nwiy8Wh1xPgdHdBWPPQDwTvJKJI3EJSvTRvx7KF68yUoxm6qKkxNCAkl/eOwWCxEfgKIoeDyesKSM\nhdpxTFVV6urqqKurY8GCBaSkpAyaR7h7ikN4FgaqqtLc3ExlZSXz5vWtgMfqNjYeRvosXtzZgN2j\ncG3m6J2v/DxaF0WSzst3o8bnph5IiSeSbc44bkxsCNlSDoRd0VLtjWBVjJv9dgsXtazkzwn7WWYc\nX+DcUFYYrdwXX8Q5zauI8door3XykcfvwvWREWMgO8nHvJgu0kxtdNldVFlVauxQ2eWj19e3wIvW\nyqTq3KhEcpt+Dxfpq0c9b7Ni4nbvGvbIfQFRd/g+D1rAezDwpjaL47qKSPJO7PobDbFsj8pifc9X\nmNTwZGEYVJmb27eQ5W7jkYxjUSQN32nZgV4d+zvh0uh5P2U5J+YkBqyrHoqHJJy9xFNSUmhqaiIt\nLY2mpiaSk0MrKDRlaEAbIUT8sGEiPb4DEYrY9vT0UFRURFxcHGvXrh3xRzwVOd1j4XQ6KSwsxGQy\nsXr1agwGAz09PWGNgB4a7e7xKWz8vIZ1sW7yo8a2Vvfa9GzvNnJLfHXAvuLB8ET3LCI1ChviQl8I\nBOLFriR6FQ2/yuoLuPvJ/niual3K7bHlXGxpntAe/iZ7OloJnphdSpLOS7espdAVSaHLzD5XJPtr\nLXzoObA3q5NUco1OzrM4WBJhZ0mEgzl6NxtqcsnUOLhAVz3q+T6Rk7nTuwovWmYbPCgeDyeo9UHP\n9zVNFr3oOK99x9hvHmusxFXoUIYVd5koEnCObQ+7IjL53DyfLcnLyLPVc9QY1vi2hMU4NEa+t2ZW\nwPeE0gAlnBXbzjnnHDZu3Mhtt93Gxo0bOffcc8My7sFCkiQ04djrmgEc1iI+mSlj4xFxj8dDWVkZ\nTqeT/Pz8UX+I00nEB5Z5zcvLG5SCEu55Do1O37yvmRabh3vyg7PSHq2NIlojc3FU8DndQ6nzGvm3\nI5Er41uI0YbXG+JRJJ7rTuXoeDc5lr7v4ysr2rilKI7fdmax1xPFr+LLMYawALEqWl5zpnFmVAdJ\nur4FT6xW5kizjSPNB+5fn7CbMWtkco1OjJrB5/qm18wel4Vb9XsCRs17VYlHvHls9GWRF+Hi2qQm\nbqmdzS3y7qD3ol1oeVGbxypbJXPdE9uy6NJGsiWugJNtRcTLodcECIRVY2JX5BxOVmpokSz8aeF5\nlDZ/yeX1H6EbwSpXgbdT15CbHMnyjOiA44ayJ26324mODjxmIDZs2MDWrVtpb28nIyOD3/zmN9x2\n221cfPHFPPHEE8yZM4eXXnpp3ONOKcISP7Tx9/huampCq9USFxcX9j2fYERcVVUaGhqoqalh3rx5\nLFq0aMx5TBd3eldXF0VFRQHLvE6k9/lIDBxPVVWe+KSabLOPo+PGrkFe4dTxQUcE18fWYZ6AC/yp\nnlloJbgyLvxBPv+yxtPh03FNxoHynjF6lb8XdPI/1RYeqUmlzGfhLwmFpOnG19r0VXtfadjL40f3\nHvQJe+C0u2c6U7BIPs7W1Y7492bFxC+9q/lGjueShA5uT2/m5poMovFwplIZ9Hzf1synGyPnt30Z\n9DGB2JywHB8aLrBOfF99xPGj8nFLOq727SMTGw9plvNy6hoqLGn8rOw14nyOQe/fGzWHWlMCv12T\nEfYGKKG60zdt2jTi61u2bBn3WNMFCZCGVnk6RDnsRHxgylhvby/AhFKfAjGW2FqtVoqKioiOjg7o\nOh+JycrpDlbEPR4PpaWluFwuli1bFjACNtztTQeK+LayDsranNyfYw3KxfxYnQWTpPC9CTQ6afPp\nec2ezHdj2oc1OpkoigpPdaWRZ/FyRNzgIDGtBP81z85ii5dfFMdxccsK/pRQyBpTcLW8fSo8b5/F\nqkgbi0yhW6JNXj3v2eLYoKsgUhr+/fv0W/e5By1/ml3HmXE9VLsNfGiN5kp5P6YxUsn8yEg8r11E\ndm8z+c7g3e8j0avRszlxBUc6K8n0Tqxpykh40PJm7HLWqk3Mp+/zuFnZyWK1g/ss6/j5kmv5Wemr\n5NkPXMfm1NXEmbScsXj0PeZQG6CI2unfIklop3FgmyRJTwJnAa2qquZ/+1o88CIwF6gGLlZVdcwc\n1ul7lWFmpB7fOp0u7ILoJ5CIe71eioqKKCoqIi8vj7y8vHEFsExGc5VgFgaqqtLY2MiOHTtISEhg\n5cqVo6awDN3DnigDRfzxT6tJM8l8J6l3zOMaXVreao3kwqhm4rWhBzU9Z03Dp0rjKrEaLP9xxFDp\nNnFNpj3gouTkJDcvr2gjzgjfby3g8Z4MvEH0KP+oN4FGn5ErJug92NSVjAqs1w22qB2qjj97FnOj\n+whSjDL/l13OmXF9gvZMWwI6VC5USoI+z8dSBg1YOL/tiwmXWH0/rgC7xsiFPRNvXToSH1uy6NRE\ncIlcNOj109RqHvO+Q6RW5c7cy3grZRUq0GyM5avYhVy0chZG3eiPXlVVxy3iXq83rMGkMxlJAq1B\nO2X/BMHTwNA88tuALaqqZgFbvv3/MTnkLfHRGpXodDocDscYI4TGUBFXVZWmpiaqqqpC7pftH9fl\nGr3ZxngZyxJ3OBwUFhZiNptZs2ZNUGlzk7Unvqehhy+ru/nFfDvBLLSfrO+LL7jy20YnsgrV3giK\nPGaK3GaKvWYiJIUVRivLTTYWG+3DAt9sipYXbGmcFtXFHMP4XNnB8GRnKqlGmdOTRv9c55tlXlrR\nzi+LY/lL+zzecKZya2wFx0QEXqw/Y8sgw+DhBEvolmivouGlnmRO0DaRrulbOPlUiTd8s/m7vIhO\nxcD6hE5uT2/C9O0+epdPy6udcZyqVJFAcN9XFXhOu5g0bw/rrIFrxgeDDw2vJ61msbuJRe7wL7xU\n4NXYFczDylp1uIdnId085X2b32qP4MnZp1BqnkWUz4lGklgfIK1sQvNR1YPeI35aI4E0jq5+BxtV\nVbdJkjR3yMvnAsd/+98bga3AL8Ya65AW8bGqrU3G/vLAsf255jabjaKiIiwWS9AiGIiD2TZUURQq\nKytpa2sjLy+P2NjYCY850Tk+8UkNUTqVi1LHXny1uTW81Gwm32Dj8e4Mij0WSr2R9Cp93wODRiXL\notAkS3zU1belYpBU8o02VhitrDDZWGa08pItFbui5dqE0N3xgdjXG8kOZxS3LrAGtSix6FT+uriL\njzqM3F8Zww/b8jna1MnP4ypZoB/smdjrtvC1O5rbkmuHNYEZD2/2xGOVtWwwVgDwmZzMX3wFVMgW\nVpqdPJpeR0Hk4HO/2BGPS9WwYYiVOhq7pBSKpAR+1PreiEFwPdoImgyxpHh7iPONvjXwSUw2bboo\nftK+Nejzj4dvTBlU6hO53bc9oMfAgpd75W08py7i7wnLkFSV0/KSSI6aPGt5xuVzTxKSJKE1zDhH\nc4qq9q8Im4GUYA465EXcL+Ajfbl1Ol3Yu3f50Wq1OJ1OiouL6e7uJi8vj5iYwA0pgmUy9sRHujed\nnZ0UFxeTlpbG2rVrx+3amwxLvK7LxXtFrVybYR+1tCrA9i4DNxfH41EkdrujKZejyI2SuTDay6Jo\nhUXRMvPMSr9wtrslvu7W8nWXlp1dZp62RvF4T9990aKy0NBLjnFs9/14ebozBYtO5eK04PerJQlO\nTHRzdHwrzzWYebgmjvObVnKJpZEfxdQS8+22wXO2WZg1CufHhB7hrajwTFcqedoezHj5sfsItsvJ\nzDZ6+FtGLafEDI9L8CgSz7UnsFZtYgHB9+F+TrOIWLmXAkcdX1nmUW+Mp94YT50pgTpTIjbNgZzq\nDG8XBdYaChx1FDjqiB0Qea4CryWvZbavizW94y+xGgyvxiwnDjenqaOPrwGuUAppJZL/0+Zw2Shp\nZRPhYPSHn2lIB7G75AgkSpI0sIj+P1RV/UewB6uqqkpScKkoh7SIazSaUcVnsixxVVXp6emhoaGB\nrKwscnJywpq6Fm5LfCD+SnEejyfk/uQwOSL+/K4WtJLK5emBi7tUOXU8UBXNRx0RSMDiaJkHlznJ\niFBHbSaSaFQ5JcXHKSk+wE2vDHt7tDxVZWBrm55yTwSX1C7iV8k1LIkIzxZMg8fAu7Z4rsx0jLko\nGQmDBq7JdHBuSi9/q7KwqSmdt3pT+El0NcdFdPCuM4lL41qxaEP/HD5zRFPlMbFSsnGZ+wSitAq3\npzexIaETg2bkOf+rO4Z2n45fycFVR/Mh8aSUz3ZNOjpV5ofZ1/b/LVbjZa5k42SpmXkaO5kaB9WK\nha+0iWzV5/PvhGUAzPZ0UmCrocBRiwpUGpO4ue2DSQn6qdPH8kXkPK6V92Bk7HsrI7FdO4ul6RaW\nzho7BSyU343b7Rb74QOZ+sC2dlVVV43zmBZJktJUVW2SJCkNCKoYxSEt4mMxGZa43W6nqKgIjUZD\ncnIymZmZYR1/Mtzp0LfwqK+vp6amZsRKceMl3IFtXS6Ft4s6OC/ZSbJx+LjdXomHa6N5vtGCUQdr\nU3V80ezjnvxeZkeOXyAjtLAsVqbYpmNVvMLFc3z8oSiCS2ryuCCmjZ8mNRCvm9h3Z2NXCpIEV8ya\n2KIgwaDwmxwrl85y8vvyaH7XtZD/7ZmDDBxl7kZWGbc7vVvWsq/XzN0tcwCV3Woilyd28MOUNmJ1\ngRe+qgpPtyWykG5Wq6PvRctIvCfN5QndUhowo0Hlu/pacrRW5mlszNPYiRuhpOtxtHAlFfhUiSIl\nhp1yIju0iXxoKGBzwnIA9KpM1iTshQO8Fr0MAzLnK2VBvf8TaRYNWPjpuuCeBaEUerHb7f2lmQV9\n3qrpvCcegDeBK4H7vv13UIX4D2sRD6clLssyFRUVdHR09PfKrqurC8vYA5kM74HdbsfpdGK1WseV\n7jYa4d4Tf6PYhk9WuS5zcHEXjwIvNJn5n9oY7D6J8xYYuDzPwOXvOjgh2UtudOgLidcb9DS7JO5Z\n5uXIJIUTUt08Uqrjmcok3rcncENiHetj20Kqw97l0/FKTxJnp/SSagrPYifH4uPppZ1sbjVya1Ec\nKhLX1+cQoVFYZHSQb3JQEOFgscnJbL273w3uUiSKXJHsdZnZ6zKzxxVF3YDqbfONLh6eV8tc49hN\nSD62WShzmfi1b2fAvWIF+FjK5DHdMqqIZr7BheRR+Z6+gpuMwdc210kqBdpuCrTdXEU5XlVisy+D\nu93LkSS4IeNSLur+iku6w1du1aox8UHUIk5VqogPMmDvBW0e6VF6TsoJrieGLMvj/g1OVt30GYsE\nGt3E2zRPFpIkbaIviC1RkqR64Nf0ifdLkiRdC9QAFwcz1mEv4hO1xFVVpbW1lfLycjIyMli3bh2S\nJGG32yfFVR9OS1yWZSorK2lvb8dkMrFo0aKwjAvhnWdPr5d/l9o4PamX2REH7ulHHSbuq4qlxqll\nXaqOn64wkRWn5cl9LmwelR8tCD2S3KvAPyqNLIlTOCKx7zrMOrhlkY/zMmV+t0/P71rm8EpPMv+d\nXMPKyODqt/t5risZl6LhuszwZkdIEvT4tChIPJBvQ0Ziv1XH3p4IXuixsLGrT1qjtDKLjA6sip4y\ntwnft+lqqSaFglgfF8U42dGl48tOPf9cWEXcKNb3QB5vTSIVJyerNcP+pgKfS+k8qltGKXHMN7r5\nS1IVn9ijqPcauExfMaFr10sqn/hSidL42BT9KX93LmRT7Bo+jF7ED9s+4ogQWpAO5a3oAtySjvW+\n4NLmiunrh37L2kx0QVqGoXQ/tNvtYSu5eiggTb07fVRUVd0Q4E8njXesQ1rEx3IHT7RGutPppKio\nCL1ez6pVqwbtSU3Wfnu4xu3o6KCkpIT09HTWrl3L9u3bwzC7A4Sz2MvGz6ro9alc/60V7lHggcoY\nnmu0MDdaw9+ON3FUug5Jkuj1qTxX7OHoRB/5MaEvIjY36Wno1XBHgWdY4NaCKJUn1nl4v0nDfYUm\nLq/N5ezoDu5IqSU6iHKsDkXDP7tTOCnRxQJzeLdzZBU21ltYEuPjrDQvkgTfTe+zoL0KlNu17LPq\n2GfVst8aSaxO5do0FwUxPgqifSSb+j6zNrfEQ+URXBjfGbSA73ZE8JXDzE3yV+iGRJfvlFJ4VLeM\nvSSSafBwX1I1Z8V00e7Tc0vDXM7TVpOkmVj6XqVi4UM5je9HlJOp7eV3UXs531vP75yLuSvlbNY6\nq/hRx8ek+gJXpRsNj6TljZjlrFMaWUhwKXsvaHMx6yXOXxp8N79QSq6Gs276ocIUB7YdNA5pEZ8s\nZFmmqqqKtrY2cnJyRqz4Nl1F3O12U1JSgizLwwLXwhnhGo49cVVVKauqZePntRwX7yLH4qPFreGm\nogS+thr4Xq6BG5ab0A+wcF4p89DtVvnRstAFQVbh0UojudEKxyWPfA2SBKemKxyd7Oaxch1PlCew\nx23hofQyFhpHd7O+0p2EVdby/cwxizGNmy3tJmp7tdycNby3ul4DedEyedEyF40xzvN1JnwqXJkU\nfN/1x1qTiMbL2coBi7oHA/dp17JVM5tUvZffJNZyXlwH+m/n9lRHMqoKVxgmZoUDbPQsxCQpXGo6\n4AVYqe/ixehPed41h0ekLL4feTmXdH3JRd27MARZRc7PB5ZcujUmLvMF5/JvJYIPNHPZsDydKFPw\nj9pQRFy404cgSWjGKKhzqCBEfJy0tbVRWlrKrFmzRk29miwRD9VN7Q9cq62tZeHChaSkDE5B9FvO\n4RLxiVriDoeD/fv3s7VRwu6F6zNt7Og2cFNxAk5Fw31HR3DqHMOgY1w+lWcK3axL8LE8LvR7/06z\njmqHhr+sHG6FDyVSB/+V6+PoJJmbdhq4pGYR96VVcnLUyJaaR5V4qiuVNbFulsWEt3wrwJN1FjIi\nFE5OCX1spw821Zk4MdoW1D44QKXLwIfWKK6S9xFJn3dht5TEXfpj6MDEzUmNXJHQOqipSpdPy4ud\niZyuq2eWZmLNSRqVCP7ty2S9qYZ4zeBr10sqV0ZUc7qhiT8683gm7gi2RC/mhtYPWO4KrrSrArwS\nu5IctZOVanDV717R5KAicdnq9HFdy8FsfnIoMwMD20LikBbxYAUpGPHq7e3tjzpfuXIlJtPIfYD9\nTPFGEBYAACAASURBVFYUeSgBYzabjcLCQmJiYsZscRqONqz+eU6kM1praysLs3P4+bZ9rIpxs8em\n5w9VMWREaXn02Ejmxwx/yL1e4aHDpfLgktCtcEWFv1eYWBClcnJa8PNfmaDy8jFu/usrAzc2LOQH\nCY38JLFxWFrbWz3xtHr1/G528BZusOzq0bPbque/cx0TKu7yeqORHq/ENbODzy9/si0RAwoXKiXI\nSDytWcyT2iVk6L28kFHC4ojhOfbPdSbhUjVcbQguyns0nvUuAFSuMFUHfE+K1s0fonZznieBe52L\nuT3tPK7s/JxLer4as8Tr9sj5NOhiudv3SVDlYHvR8oY2mxNzEsiIHV+aZqjudBGdfgBJAq1++ga2\nhZNDWsRhbNHzi1egH83Adps5OTkkJCQEfd7JYDzj+iPmOzs7WbRo0agr9XAvOkKxxHt6eigsLCQ5\nOZm1a9fy6u4mmm0eZsWo3FcZywmZOn5zRCQW/fB74JFVnt7vZmWczJr40K3wLa06yu0aHljuGTWv\nfCRSI+CZIz38dq+Ov9elU+SK5P70qv59ckWFJ7rSybV4OTouOAt3PDxVZyZar3Je+sS2EjbWmlgS\n2csKc3DWcYtXxxtdcZwtl+FDww26k/laSuacmE7uTKvDPEKeukPW8FxnMsdrm5ivGV9Q4FA6FQOv\n++ZyprGRVO3YEeNHGjp4Sf8Jd9vzeTr+SMqNydzS9j4RamDvxcuxK0nDwQnqyB3chvK2Zj5W9Fyy\nfPRGJyMRqjt9Mho5zVgkSVjihwv+XPGRfjTt7e2UlpYGbLc5nfG7/TMyMli7dm1QQX7hLs4S7Hg+\nn4/y8nKsVisFBQVYLBZkReXhrZUYNCq7ekzcuMzElYsMAa/jzUoPrb0qv18cel15VYVHKozMMauc\nMSu0e2HUwm+X+lgcq3LvvljW1y7q3yf/0B5LldvIgwu6guq+Nh5qnFo+aDfx/+a5iJzAr/rDVj21\nTi03z2kLeo7PtiUgq5CldnK54Wy8kpZ702r4bmxnwGNe6ErEKmv/P3vnHR1XdXXx35teNBr13q3u\nbsuWCyb03hJ6D2BKvhAgoQVS6MFACMVAAhibEsD00CE0m+re1XvvGml6fe/7Q5Yt2yqjmZHtYO+1\nZi2MNHfu07x3993nnrMPV2qDV+GvebJwSwJXav3PPtcKIn8L20a+08zj5HGTKoq72j8kybuvw1yJ\nOoFSdSK/HyZhbziIwBvyQnKjlKgtLaxbV4dWqyU8PJzw8HAMBsOoJWSBhtPT09PH9Z6fM4SDvMQs\nlDjkSXy4s2un00l5eTmSJAXlWnYgMDh3wK+w/yAmQon7M153dzcVFRWkpqbu4Wz34bY2Wvpd6BQC\nTxytpzhh5FvV45NYvsPFNKOPBdGBq/BVXQrKzHLun+4JKhwtCHBhho9cg7jrnPzBhFqWmRJJ0/o4\nISa0DWwAXmrWo5DBRWnBjf1ig5ZklYfjjP5lcFt8Ml7viSJZtPCQYh4FagePplSRqR45GuASBV7s\niaNY3sUUeXAtQi2Sgje9WRyn6iBDPr5yPUGAy7X15Mkt3Gadwe9SLuSOjk8ocuyptt82ziYcN6eL\n/jVl+UFIpokwHj5yEjMmxyFJEg6HA7PZTFdXFzU1NUiShMFg2EXser1+173v8/lQqVRjfMqeOJyd\nvjeEwyT+c8FY4fShrm2iKNLQ0EBbWxs5OTnExsbur2kGDUmSaGpqoqmpidzc3HHPfaK6jo0Et9tN\neXk5Xq93n82GJEms+LGRGK3A8hP0pISN/jC+X+Om3S5xf5EzYIUrSfB0tZpUncTpKaFJSBx6Tn5j\nazYAf83pJ9RJsyaPwLvtOk5PdBOnDjyZcGufnE19Cu5MavPbwOaZ9lhsohybLJzLojq5Ob51RDvW\nQbzbF023V8kDmsqA5zqItz0ZWCUFV2lrx/7lETBP1cNrxh+5yTqLvyScya97f+S8/gGzmmZFBD/p\ns7jctwOtn9nsr8kLSTQoOS5/wNxFEAR0Oh06nY6EhIFSM5/Ph9VqxWw209DQgM1mQ6lUEh4ejt1u\nHzeJW63Ww9npQ/G/6dgWEH72JD4WBpX4YMOPwfPY8YazhsNgSHkiwvBDk/EGE9ciIiICdlzbX0p8\naEvWkexdv67oprzDyr3ztWMSuNsn8UKJi5kRwavwkp0qPJQeEYPn5Cd8rabLKfB1t5rT4hyEK0Pn\nZreyRY9TFPh1enAqfEWDhnC5yK+i/Ct9e6snghXdMSgEkaWpdRxlGFu9u0WB57rjmSY3USQPLrnP\nIcl51ZvNfGU3BYrAar8HkSJ38HL4Gu62TmF51EKq1XHc3PUF7xhnokTkXNG/DUeJEM0WIY7b5qWi\nlI/et8FoNO7RFMntdmM2mzGZTDQ3N9PU1IROp9sjDD/SunSYxPeGgBCCNfx/AYc8iQNUVVUhl8uZ\nMWMGOp0uZOMObhBCTeKDKncwca2vr4/CwsKgHuL9ocQdDgelpaWo1eoRW7JKksQzq2tJCZNxUsbY\nLVvfq3bTYZf4W2FwKvypajWpeokzQqTCh6LcLNDlFDg6Vcl3LXD2plientxLbljwRi9OH7zSqueI\naA85YYHPvdEu44sOFVfFdo/ZMMXuE7ivJYn3TJEAPJxc7xeBA7zfH0W7R8WfNBuDzgt4z5NGr6ji\n6rDga8wBdIKPh8K2UuA08yS51KuiaVMaOcVX67fF6quyQgwqGWfPGH/PcJVKRUxMDN3d3SQlJWEw\nGHbZIXd0dFBdPRDOHxqG1+l0CIKAzWY7TOJD8D/qnR4QfvYkPlIilCiKNDY20t7eTnJyMnl5eSH/\n7EESD6Z/+EjjdnR0UFtbS2pqKrm5uUFnw4e6YcnQ7HRJkmhsbKSlpWXMDP9vq3vY0Wrhr8XaMW0q\nXT6J5SUuZkX6mB+ECv+6U0GpWc4DMzwhD3UD/KtKgVEtcO8CPVV9Pm771sp5m2N4MK+Pk+OCU8/v\ntevodcu4OjO4DO8V9RrkAlw6hrlLpUPNTY3p1DpVGJQSGQoHJ4X7d67tkeC57gQK5X0skHcFNV+X\nJOMlby6zlSZmK0NnmiMIcIW2jly5hZsss/AgUCD5V2rXTBirZalcWZSMThW4ChxMbBMEAb1ej16v\nJzExcdfPLBYLZrOZuro6Vq1axTvvvAPATz/9hNFoJC5u/BnxAI899hjLli1DEASmTp3KihUr/M6p\nOeggHDpn4v876dYhhMlkYu3atXg8HjIzMyesvnIiDF+cTidWq5W2tjaKiopIS0sLSTlbqPuUD24K\nLBYL69atw+l0UlxcPCqBS9JARnqCXsapmWNvfN6tctPlkPhddpAqvEZNml7i9OTQq/CyfoHVHXIu\nylejUwpMj1Xw75PDyYtS8PvSSB6pMeANcO/kFWH5TovVOZGBq/oel8B7rWrOijQRpxx+HEmCt3oi\nObc6m35JxVU5IhaPwHUxbX7/7T/uj6LZreJqZUXQKvwDbxpdopprNP4lm40XM5QmlIJEmEzkIcU8\nlsumjNl09HVZAXKZwEVF4zN32RujNUCRy+VERESQlpbGlClTuP7663nxxReRJInt27dz4YUXMn36\ndNauXTuuz2xpaeHJJ59kw4YN7NixA5/Px8qVK4O6jgMNQSY7YK/9iZ+9Eh+KwV7ZLpeLadOmodfr\naW5uDnk70kGEksQH1WxzczM6nY78/PyQ9g+Wy+Uh7ToGu13XxqpRH8SaOhNbms3cMUeDcoz0cKdX\nYkWJizlRPoqDrAsvN8t5cIZ7QlT4c1UKwpQC5+ft/q5idTKePc7APzY6eKESSqxKHiswEaka39//\n8y4NTQ45t+bua7E6HrzSqMEtwpVxwytOq0/GXc1JfNwXwbxYib/NFrn6B4EcjdPvMLpXgn91JZAn\nN3Ok3D/Hs5HgkQRWeHKZpuijWBl60xyAt52p2CQ5L6eW81ZfLM+bp1MixHCX70fC2bfGvw81H8sn\ncdrUeGINwT2X4z2CS09Px+fzsWTJkl1rTiBRNa/Xi8PhQKlUYrfbSUoKbjNyIDFQYnZoaNSf/VUO\nns02Njayfv16YmNjmT179i71rVAoJsQeFUJH4v39/axduxaXy8W8efPQarUhd4ML5Zm4yWRiw4YN\nAMydO9dvO8inVtUSp5Nx5qSxM3PfqXbT7ZS4fhgV7hGh1irDNsbeTNx5Fp6ulzg1wLrw0VBjEfhv\nm5zz8tQYVHs+akq5wO1zddw1X8emfjVnb4qjxOL/nlqSYFlTGJl6H8fGBW6xavPCa01qjjOayRzG\nYrXUruHsqmw+7Y/gd4Uizy6U2G4auLZrotv9NsT5tD+SBreaxSFQ4R97U2kXNVyjrQ55vT0MWOO+\n4spint5Ckd7GkqR6/hLfyDp5ElcqT6GKiH3e844sBxdyLi9OCfrzA6kTh90NneRy+biP8JKTk7nl\nlltIS0sjMTERo9HICSecMO45HDwYSGw7UK/9iZ+9EjebzWzbto3IyMhhM7dD0Y50JARL4l6vl6qq\nKsxmM5MnT96VuDIRYfpQkLjX66WyshKbzcb06dPZunWr34pifb2JDQ193Dpbg2oMFe7wDrizFUd5\nyTP4WNcjp9wip9wio9wy4LjmEUEmQL5BZHakh6JIH7MifcQMKcH6qlNBhUXOkglS4c9XK1Ar4KL8\nkZXZGZPUZEfIuWW1jYs2x3Bndj/nJjrGJMcfTCrKrErun2wdt7PcULzVosbilbE4dk8V7pPg9Z4o\nHmpNJFIjsOIIkdkxA5uH5ysEUlVuTjL6dxbtk+Bf3Qlkyy0cLW8LfLKAVxJY7smlUGHmCKX/trDj\nwYeuZLp8Kh6Mrgd21v1HdVGgsXNT6ySu5iRu967lZGnAXMaJnHcU+RyZFcmk2OCP5iRJGpcSD0UE\nzWQy8f7771NXV0dERATnnnsu//73v7nkkkuCHvuAQDjcxexnA5lMxpQpU0Y0QjhYlfhgNmp6ejr5\n+fl7nHtPhC97sGN2dnZSVVVFeno6BQUF4z6nf2Z1LdEagV9mj67CfaLE3T/Z6XFKIMqZ99VulR+l\nkZETpeD8VCWZEXJaLD62dHp4s1nGKzsbW2XoJWZHephp9LG8fkCFnzIBKrzRJvBxi5wL8tVEakZf\nTAqjFbx6ioE7v7dxV2UEb7XpuTO7n1mjNEh5vtFAnFrk9MTA7VvdIrzUoGVOmI3p+t3e5t9bwnik\nLZEKh5oj4iUenC0SuXMfsqYLdvQJ3JPY7nct+X/NEdS6NDyo3hHUhgPgM28yzaKOx/SbJkSF+yR4\n0TWJyVo783WWPX42Q2fj7YxSbm7J4l77Anb4YrhJ3MgnsixMkppfz08N/YTGgWByY7788ksyMzN3\n+Uv86le/4scff/wfJnEB4RBJbPvZk7jBYMDjGXkxHGr2EmoEQuKDjVYUCsU+PcqDGXcsBEriLpeL\nsrIygBHnOxY2N/XxY62J38/SoBmFGX5o9fCPTU7q+kXUcpidrCUnUkFulJKcKAXR2uEfWo9PorzH\nw5ZOD1s73Py3U8Y7zQPqZXaUj34PRIcuvQCAF6rlA9neBf5l90ZqZDxzbBif1rtZutnJRZtjODXO\nwS1ZZhI1e34v281K1vapuC3XjioIsfFJm4p2p4x7MwcyxSscah5uS+QHSxjJOnhkjshJyexBls9V\nQKzCM6ql6lCIO1V4hszKsfJWukQ1DWIY9VIYDeLAq55wekQVBbI+5si7mCPvZqpsILFsKHwSLPfm\nkqOwcpSyM/ALHwVfuhNo9Gp5PL5m2E1CjMLLC2mVPNaZzIreXCrk0fSiYUqCnqI0475v2A/weDwB\neUMMRVpaGmvWrMFut6PVavnqq68oKioK0QwPDA6XmB0imKiWoeMde6hb3FhlWBOlxMezmZEkidbW\nVurr68nJyQm4rAXg6VV1RKgFzskZXoVXmnw8vtnJmjYvYeoBon7mxCimxPrnaqWUC0yNUzE1TsWl\nU/R4fCLn/acHq0diiwlO+UbO7/I8XJDuC0lYvd0B7zUrOCtbTazO/wEFQeCUTDVHp6p4scTJK6Xw\nVY+Gq1OtXJlqZXCP8nzjQKOT81ICL08TJVhWryVP6yRH7eSOxmT+Y4rAoBS4barIBZmwd5XU5h5Y\n3y3jdj9c2QY/49GORCqdWpIFO8c4T8Uq7h5ULZNIV7uZonERpXCy1abnOXsUz5KPRvAxQ9bDHHk3\nc+Td5Mv6+dqbSL0vjIfDtgSt6IeDJMELzklkql0jtpIFUAhwa3wL07Q2bm/NxC3J+MP80FSJBAKL\nxRK05WpxcTHnnHMOs2bNQqFQMHPmTK655poQzXD/QxAOm70cMphoJT5aFGAQg927YmJi/HKLO9BK\n3G63U1JSgl6vD9ghbhCbGvv4rrqHG2dq0O6lwrvsIv/c5uSDWg86lZzLihJ5e2sHR6aq/Sbw4fBF\nvYtWq4/7j44hK0rJ42tM/G0HvN2o4M9T3BRFB3fG+EKNAiS4vDAwea9VCPxmupazJql4YrODpfUG\n3m7Xc2tWP/l6D1/sbHSiD+LpXd2lpMYm55hwKydX5uFD4PJsiavzRIwj/GmXVQhEKHycFzV6Rrgk\nwSprOE90JFHh0iJDIlUv8QutmUyNm0yNi0y1m0SVdx8y7vfKWG/VscasY401gqWOgc2hHh8gkSBz\ncpyqPfALHwU/emKo8Bq4L7ber03CCYY+/qlyYdMYd1msBotAzrdD5dZ2zz33cM899wQ9zsGCw2fi\nPxOMtTueaCXudI6sljweD1VVVVit1l3du/zBgToTHxotKCgoIDIyMujPXfpNDVEagfNydzOHwyvx\ncqmLl8rceEU4Y3IsF85I4O1tHTg8ItfODFx1eHwSz2+xkhut5BcZWmSCwD9OiGV1g4Mn15q47EeB\nM1J83FzgITYAn4tOJ7zVoODULBVJY1jGjoXEMDlLFoVxXq6Hv29w8IfSSKKVPhQCHB/vRpIY97mw\nV4Ram5wHynXIkPjabOTkFIkbC0VSRsnJKuuD1R0CN8R1oJMNf59IEnxvNbC0K4ntDh3RO0vmHkhv\n45cx/pWiGRUix0VYOS7CCnTS7ZGzzqLj7W4jP1rCsIkK7rRO52Z9OXGywFuuDoflzizilR5ON/p3\nVLDOHkalS8tfjkkb05jIXwTawexw85O9cFiJHzqYCEIcxEgbBEmS6OjooKamhoyMjHEngk3ExkMQ\nhFHHNJvNlJaWEh0dHbK2rBsaTPxYa+IPs3ar8LXtXv76o4Muh8gRmRFcMSeJxHA1vXYPH5R0cWKW\nhuzIwB3wPqx20Gr18cj8KGQ7/+aCIHBUho7iZA0vbzXz+g4zX3fIuT7Xw0UZ4wuxL6tWIEpw5ZTQ\nOV3NilfyyskKXilzsnTzwKbwnDVGYtQS08I9TDV6mWr0MiXch3GIJ7soQb1dxo5+BTvMA69yiwLH\nzq85VSfx8FyRqX7sxZ4tFzDIfVwSta/TmiTBGlsYS7uS2GzXk6SVuGeKi1fqlYTLPJwRHbiveYzS\nx0mRFv7ZHkOG1sPJUVZeaEvgu/44fqup5HxNIwoh+OzsrZ4INniiuD2uCZWf4z3fk0i0TsGZ0xKC\n/vxBHCbx0OFwYtshgok8xxqObO12O2VlZahUKubMmTPubkUwsPHwJ0w/Hsjl8mE3M4P+7CaTaY8y\nt1Dgya9riNHKODtHhSgNlI09s81FilHDI8emMjlh98L0xpZ2vKLE4umBL1ZOr8TybVamxqmYn7Iv\nyWqVMq4tiuCUHD2PrzGxpATea1LweJGbdP3YC3unE97cqcJTDKFdQOQygR6HhFyAB4+OpNMmUtrt\npqTbw9fVu4+DMvQiBQYP3S4ZJRYl9p0/0igEcqOUnJGrZGO7i06rl3eOkdD5sR+q7Icv2wR+G9uJ\nYS9f9Q02PU92JbHeFka8RuKvU9z8KtXLV+1yqq0yHs3sCqqtK8B/+wxUOdQ8kt3J6bE2zoy1cn99\nDA/3FfC+O4U/6UqYrgyupekLjiyMch/nRPpXtlbi0PGjLZybjk5FHcL6xEBJ/LBv+p4QBOGA5Sjs\nb/zsSfxAfpFDSXxoKDo/P5+oqKigxh0tTB8IhnqdD2Kws1tycjJz584N6d9yTV0va+v7uGW2Bq8I\nd/5gZ3Wzl19kRXDDojS0yt0LWYfFxaflPZyeoyU1PPBb9t0KO112kb/+ImLUa0k1Kvn7CbF82+Bg\nyQ+9nPedmr/PcrMobvSIzbJqBb4Qq/BB9DpF3qlyc2KWliPTBvvbD8S/LS6R8h4Ppd1uSrs9bOn1\nEKWRcUq2kvxoFQUxStKNChQygfJuN2+U2bipUPSLwAH+VQ56mcil0btVeLdXwV9b0/jGYiRaLXFH\noZvz0ryo5QNZ5E9XKZmkdXNSpGWUkceGKMFTrTFkad2cEjPQLzxD6+X5/HY+79XxYH0Ml5nn8St1\nEzfqKomQjX9zW+41sNoTx/UxrehHOCrYG8t64glTyThv1vgbnYyGw0o8dDisxH9GGKu39URhkMRN\nJtOuNqehCEVP9Jm4x+PZZU87c+ZMtFrtGO8eHyRJYunXNcRqZUyLkXPxZ1babCLXzU/h9MKYfQj2\n1U3tyASJK6cFvlDZPCIvbbdRlKRhVuLYJCsIAr/I0JETreKOr7q4bi3cmO/h6mzfsOfQgyr8tAlQ\n4QCvlblw+yQun7av4jKoZcxJUjMnaexEupe2WzEo4fws/z632gxftApcE9OBUT6wIf3OYuCO1kys\nopyb891clOFlaHXfp61yaq0yHs8KXoV/ZjJQ7VTzaE7nHmMJApwUbeeIiCaebork5fYUvvYkcpO2\njDPVLePKXl/mmIRe5uOSKP/K1urdav5rieTKBckYNKFdQg8r8RBhoI3ZgZ7FfsEhQeJjYaL6fkuS\nRF9fH263e5dXeygwkdnp7e3t1NTUkJmZSWJiYtDqe2jf80GsqTOxobGfUzKUXP2lnTC1godOnURh\n/L4k3dTn5OvqXi4o0BGvD5wc3yi10+cSuXb2+Gp5kwwKnj0tnge/6+Xxcjul/TIemOHZJzN8IlW4\nxS3yZqWLYzI0pBsDf2Tr+jysanByTZ6EwU8V/lyFgEYmcXl0J25R4B+dSbzUE0eOQWT5TAc5hj03\nx14RnqlSkqt1cUJEcCrcJ8HTbbFM0nk4Kdo27O+EySVuz+jlrFgL99TFcLdlKp+7E3kobCtGP1R5\nrVfPl+54ro5uJ1zu3zO1oicepVzGJXOSx3U9/uAwiYcOB3timyAIvwcWAxKwHbhCkqRxh1gPja3K\nGAg1KUqSRFtbG1u3bkUul1NUVBTSTmkTocQ9Hg89PT10dnYyZ84ckpKSgibw4UL0kiTx+FfVaBXw\nSb2HvDg9S3+ZNyyBA7yysQ2NQuCyqYGrcLNL5NVSG0ekaSmMHX/Zl0Yh4+6jovntnAi+bJdz0Q9q\nGm27/zYTrcLfqHBh80hcPjW4hfqV7VY0crhkkn9RqVoLfNoMF0d10edTcEF9Hi/1xHFRuoc3Fjr3\nIXCAT1rl1NtkXJ/YFXQt96cmAzVOFdcnm8ZU9Hl6D69ObuPuzG42eKO50LyAKu/Y98wyRxYamcRl\nfqrwTo+S//TH8MvpCcSEBV7mOBL+10n8QEQ8h4XAgO/ygXqNNT1BSAZuAIokSZoCyIELArnUQ0KJ\njxVOH6wVD0Xfb7vdTmlpKRqNhqKiIrZs2RLyc/lQd0drbm6mvr4ejUbDtGnTQjIuDB/h+Gh7B1ua\nB7KVz50ez2WzE5GPcNNXdtn4vq6Pq6brx7QuHQ2v7LBhc0tcPStwRy1BELhoajjZUUruWtXDed+r\n+ftMN0fEibwwgSrc7pF4rdzFwhQ1udGB35+tFi+f1zq4OEvaZaE6Fp7fqcKj5W7Ors1HrRB4qsjF\nMfHD33uDKrxA59pZIhY4fBI80xZLjs7DiSOo8L0hCHBBgoV8vZvfVcZzqXk+9+m3cbx6+K5pTT4t\nn7qTuDSqkyiFf14RL/fGDdTUzwu+0clw+F8n8cG1rrOzE7PZjEqlIjw8nIiIfZvGTPBMDnolzgD/\nagVB8AA6oDXQQQ55hMLwRRRF6urq6Ojo2FVDLUnShJSvhUqJD7YKNRgMzJ49m9LS0hDMbjf2nqck\nSSz/sQGlTOCWo9NZlDlybZMkSSxf10qkRsbFkwOPYnTafLxRZueESTqyo4JXTnOTtSw7PWHgnHwd\nXD3Jw5uNE5ORDvBulYt+l8SvhzkLHw9e2THQKOXyHP+UUqMVPm6CNJWbhzpSmRvt46EZLuI1I7//\nwxY5jXYZz0wKXoV/0htOrVPF47kd4x5rhsHFO1NbuKEynlssM1nsq+H/tFX7qPnljiwUgsSVUf6Z\nx/T75Kzsi+PEwlhSI0ObJzKIQEjcZrMdFCTe09PDqlWraGxspL+/n97eXnw+H/Hx8cyfP59Zs2YR\nExMjSPtDrgsCHMQkLklSiyAIfwcaAQfwX0mS/hvIWIdJnOCVrclkoqysjPj4+D0S1yYqMz7Y+Q5u\nODo7OykoKCAiIgKv1xvyDcfeEZCvyrsobbNw46LUUQkcYEOzmW1tVm6Za0CvDFyFL9tqxSdJLJ4V\nOiWQHD5wTv6373p4tnogcnfxKJ3KAoXLJ/FKmYvZCQOWsYGi2+7joyo7Z6VJxPvJPQ9uExCBRreG\nm/LcXDXJO2pI271ThU/WOTnaGLwKf7o9hjydmxOi7AGNEafy8XJhK/fVRbOscxLlvnAe1G8lXDaw\nWW/zafjAncx5Ed3EKv3bwL9uisUuyrhqAhud+Hy+cUcED5bs9G+//ZbVq1ej1+vJzc1lwYIF+Hw+\n6uvrefrpp+nv7wc4Ffhof8znADu2xQiCsGHIv5+TJOm5wX8IghAJnAlkAn3AW4IgXCJJ0r/H+0GH\nBImPRaaBKnG3201lZSVOp5MZM2ag0+kCneK4EIwSH7R4jYuLo7i4eNeGQyaTTUiy3CCJ+0SJx76q\nIdmo5rickX3hB393xbpWksLknJUb+N+0vt/Lh9UOzi4wkGQI7a2uVcr47ZwIVjU4ECW483sbJJaC\ngQAAIABJREFUjx4VRmoI1fiHNW66HSJ3LQpOZb1WYsUnwRV+qHCfBI/ugO86BMIUEs/PdTI9cux7\n7Z1GBS0OGXdndwXdXeyD3nDqnSqeDECFD4VKBvdN6mFymJv762K42LKQx/UbmKSwscKRCQhcGe2f\nCreJMl7ujWdBRji5caHLb9kb/8vh9OzsbE477bRhNyG/+c1v6O3tJTo62iUIQpQkSf7Z4gWKA6/E\nuyVJGq2DzHFAnSRJXQCCILwLLAAOk3ggGK+yHUxcq6urIysri4SEhP1ajx6IEvd6vVRXV2M2m4e1\neJ2IMrzBM3GAj7a3U91l44/HZIx4Bj6IVTUm6k1O7jvSiDKIGqVnNlnQKAQunx4+9i8HgJe3WZAJ\nAr9flMZza5u59FMLDyzUszA5+NwKjyjxUqmTyTFKihIDV+H9TpH3KuycnCKRNoZY63LCHzcIrO0S\nkAFvLHSQ6YfAc/jgn9VKigx2jgj37/x6JLhFeKotlkK9m+MDVOF744J4CzlaNzdWxnOJZQG3aUt4\nz53KmeE9JCn9qyt/0xRDn0/BCSkS69evR61WEx4ejtFoJDw8POguYoMIlMTDwyfmHh8Ppk6dCsAL\nL7xAZGQkixYt2tXaVJIkoqKikCTpi/0xFwEQDu4Ss0ZgniAIOgbC6ccCG0Z/y/A4TOKMT4nbbDZK\nS0vR6XTMnTs3JMlw48V4lXh3dzcVFRWkpqaSl5c37IZjIjYhg/N0e0WWflNDVrSWIzJHD2u7vSKv\nbGwlP1rJcRmBJ4pt73SzutHF4llGIkdoURoMWsxePqq0clJ+DMfkRlOYGMYDX9Zy4zdWfjNdwxVT\nNLtsXQPBJ7VuWq0iNxePbkwzFl4vteLwSlydO/oG7YcOuGOjDItnYAG8NNPjF4EDvFavoNsl8ERG\n8Cr8nZ4IWlxK7spsD2m/8NnhLt7eeU5+t3UaAhJX+anCXaLAit5EijOMnP2L6QA4nU7MZjM9PT3U\n1dUhiiJhYWEYjUaMRiM6nS6g7+1/WYkPzr2hoYGPP/6YrVu3smjRIqZPn76LzPcbDrwSHxWSJK0V\nBOFtYBPgBTYDz43+ruFxSJB4KJqgiKJIbW0tXV1du86R/f3sUNegD1e6NRzcbjfl5eV4vV5mz56N\nRhP67OnRMKju39ncSpPJyT0nZo1JbB+VddNp9fDXBZEBk6AkSTy10UqUVs75kydmcVuxpR+5TOD8\nGQO+2QkGNY+cnsfS7xp4ZquJ0l4f98zXE6Ya/zV4RIkXdjgpiFGyICXws/Z+l8hbZTaOT5LIHkGo\neUR4qlTghSqBzEgVeWEKtrTauWqSfwrV4oHna5QsCrcyO8wR8FwBnKLAM20xzDY4WRQR3FjDIUHt\n4/HcDo7fnIpPEniwM5WHkuqIGKM+/N2+GLq9Ch5amL7r/2k0GjQaza4WvKIoYrFYMJvN1NXVYbfb\nd2VmD6p1fzb8gZC4w+HYb0d5o0EulyNJEvfeey9Wq5WVK1dy7733YjQaufzyyzn66KNHbbEcchzk\ntquSJN0F3BXsOIcEiY8FhUKBwzHyotHT00NFRQWJiYl7nCP7g8ENQqiNZEbD0HD/pEmTiI+PPyD2\nszKZDLvLy9Orapkcr6coZfSQn9Xl5Y0t7RQnqZiTqEaSJDrtIlUmD9UmL9W9XjrtPvKilMyIVzEz\nXknUMCr7hxYXWzrd3DI/El0QSXEjoaHPw+c1Ns6cEke0fneoW6OQcctRGeTG6lm2tpnLP7fw6JF6\nMozjW5Q/rXPTYhW5KUgV/mapFZtH4rr84Td8LTa4dYOMbb1wen44Z+SHc81/mrkyy0OMn3uHF2uV\nmD0CN2Xv2xhlvHi1M5Iuj4J/5Aav6EfCv9vCkSSB3+a4ebbayHn1hTyeXE2hZvjn3yPBst5EZiQb\nmJM+comiTCbbpcJTUwcS31wu164s7fr6+j3Uenh4OHq9fp/vNxASlyRpv64vo2Hweux2OwsWLCAt\nLY0777yTG264gZSUFNavX38m8MGEZ6gLAsgPDXo7NK5yDIykxAeVrMfjCdh+dHDs/RV2dzgclJaW\nolarD1i4fxCCIPDWlg66rG5uPSp9TEJ6YV0LFpePMKWSaz/toabPh8W9+9ggLkxFtE7F+9UO3iwf\nOC9NNyqYGa9kZryKmfEqYrQyntloJSVcwel5E5Oxu2xzPyq5jHOnxe/zM0EQOHNKHJlRWpZ8Xcel\nn1m4b4GOo1L9O9f2ihIvbHeSF6XkiCBUuMUl8kapjWMTJfKG4Z4vWuCvm2WIyLjrmFiOyTJwz1ft\naBVwpZ8qvMcFL9YpOCnSzGRdcG1BrT4Zz3dEszDCwZzw0PYFGESPR8ZrHUZOTfLy2xwPR8T6+P0m\nDRfX53NXQgNnReyba/VhfzRtHiV/OWLs+3dvqNVq4uLi9lDrVquV/v5+6uvrsdvtKJXKXeQfHh4+\nbhI/aMxVhuDJJ5+ktbWVrVu3EhcXx2OPPcaiRYtoaWkhJSVlKfAFEJqEh9EQovawBzsOCRIfb3a6\nJEm0tLTQ0NAQtJKdyH7lQyFJEo2NjbS0tJCXl7d/w1YjwOmDl9a3MTvFwJSEkQm1zezi2Z+aWdc0\nYALzU6ubjCgdR2RpyYgaeKVHadGrBm5XryhS022npN3K9jYLX9Rb+U/lgJIyqgX6XRK3L4wMWY/n\noajqcfN1nZ3zZyRg1I68QZqWZOCJs/J54Mtabl5t48J8L9dO02IYI7z+aZ2bZqvIw8cYg1PhZTas\nHonf7KXCrR54vERgZZ1Afqyau45OIClcSU2vi2/qrFyT7SHSzzy6ZTVKXD64Icm/zl+j4aWOSPq8\ncm5Knbik5RdajLhFgeuy3QBMjxB5a6Gdm7douLMtk20OPX+Mb0Yl21lRIcFzPYkUxOs5YpIf/VrH\ngEwmIzw8nPDw8D3UutlsxmQy0dDQgNlspqqqahexD6fW98bB1rFry5YtnHzyySxZsmTX/xNFkeTk\nZIBHJUmaeAIHkB28Z+KhxCFB4mNhKNFarVZKS0sJCwujuLg46KzT/UHiFouF0tJSIiIiKC4uHnc4\nbqLwQYUVs9PH5UVJw/7c7PSycks7H5V2I0oSMgH+duqABetoi5JCJiMvLoy8uDB+NS0BnyjRYHKw\npbmfVzcNmB49ta4Prwhn5oWNmQ0/Hizb3I9eJeeXU+PG/N3YMBUPn5bLsrXNrCzr5rN6D7+druGM\nSaph5+TdeRaeG6VkUWrg+Qs2t8jKUitHJUjk70zd8IjwZh38q0KGyQUXTI1gcVH0ruz/lzb1olfA\n5Zn+qfA2h8DrDQrOiu4nVe2m3qmk3qWiwamiwaWizqmiwa3GKwnM0VtZEG5nnsFGsnrfBNI+r4wV\nndEcG2ljapg74OseDUNVeGbY7o1NtBqWzXHyRKWSF2rjKHXpeTy5hgSlh8/MkTS61TwegAr3F2q1\nmtjY2F2JX+vWrSMlJYX+/n4aGhqw2Wy71Prg+frQ6JrX6z1oQumDWL58+a7/HswHGpyjJElP7JdJ\nHOSJbaHEYRJnQIl7PB6qqqro7u6msLAQozFwi86hmEgS9/l81NbW0tPTQ2FhYUjKTIZrWBIIuq0u\n3i+3ckRmBNkxeybduL0iH5R28caWDuweH9OSYtja0s3Z0xKYnDD+RDS5TCArWseGpn7cPokbjpzE\nqqouHv3JxAeVNm6ZH8mUuODNWEq7XHzf6ODS2YkY1P49OiqFjP9bmMYJeTE891MT96+18Vali1vn\n6JgZt+cYn9e7abKILDk6eBVucQ+ocEmCz1vgiVIZTTaYlaTlobnR5MXs3iRU9bhYXW/j/3I8RPih\nwi0euHGjCo8Ia616Zm7Owyvtnq9BCel6iZmxA5+/ptvIx6aB5ylV42F+mJX5BjvFBjtRSh8vtEdj\n8wncmGYK+JrHwt4qfCgUMrg538NUo8id23WcUz+ZRxKrebYniewYLUfn7b+oliAIu9T6IAbVel9f\nH42NjXi9XsLCwqiqqsJgMITE6KWvr4/FixezY8cOBEFg+fLlzJ8/P6CxBnOABEE4sBuMg7vELGQ4\nJEh8rAWxv7+fnp4eIiMjx524NhYmisR9Ph9r164lMTGRuXPnhmTOg9nkoSDxZ1bXDbTOLNrdb1mU\nJFbXmHhpQxudVjdTk6L51bRsXt9UgVGj4Nydmd6BwGT38PbWNuamRXJUdiy/mBTDj3W9vLiugWs/\n6uC0HD3XFUUEVW723MZ+jBoFZ0weW4XvjewYHQ+dlst3tSaWr2th8X8tnJCu5MZZOhL0MnyixLId\nLrIjFRyZFoQK94i8XmrlyHgJmxcuWC1QYhLIilTx8BHRzE3Zt/TpxY09hCvhsjFUuNUD/65XsKxW\nhd0LRpXE5Gg5p+hF0sMk0vWQESYRqdozMViSfNRYYE2XjDXdcj7pjuTN7oHw9CSti3qniuOi7OTq\nxt8L3B+MpML3xgmJPrINDm7YpGFxUy4SAktOSg+qVDAU2Futi6KIzWbjxx9/5KWXXqKkpIRjjz2W\nefPmsWDBAk499dRxf8aNN97ISSedxNtvv43b7cZuDzzifVBEAg8r8UMDLpdrVwmWXq8nIyMj5J8R\nahL3er1UVlbicrmYM2dOyCIGsLuuO9gNQX2PnZUbWjgpP4Zk4wAhVXXbWfp9I9XdDtIiDfzh6CkU\nJESxubmTys4+frMgbdeZdyB4fVMrbq/EZXPSgIENycKsaGalRvDWlmY+3NHOqgYH1842BhRi39jq\nZH2rk8XFyehUgS0OgiBw5KQo5qZH8PbWdt7Z1sHqZjO/nqwmXiej0ezjb0cFXloH8E65DbNLwuyB\nK7+XEatXcMeRURyfbRj2msu6nHzfaOd3uW7CRzjit3kHyPvFOhX9bojWyhAlkQ+P8RLtR4BDECA7\nHLLDRS6ZBF7RR2mfwE9dAivrVfgkgR/7tazsMHBenCXk+UijqfC9kRUmsXK+gxNX69Bp1ZxYuJ/r\nm/2ATCbDYDCwePFiFi5cyKOPPspTTz3FmjVrqKysHDeJ9/f38+233/Liiy8CoFKpUKlC06FtsPQu\nLCxs/5P7YSX+88Vg567Gxkays7OJi4vjp59+mpDPCiWJd3Z2UlVVRXp6Ona7HbU6tH7dcrk8JP7p\nSz4uQSmDi2YmIEkSn5T38OxPzRg0Kq6aN5m5GQnIBAGvT+SdLVWkRmg4MT/wxbLR5ODzii5OKkgg\nybhnBYFWKeeyOekckxPH8z/V8ehPJj6stHHbwkgK/KyjkiSJf27oI1av5NSC4Bd1jULGJbOTOCE3\nmuXrWnh2Wx9yASI0MmSCRI/dR7RufBnKLRYf27vcLNs80MO72irn2jmRnD3ZiFox8mK2bH0PESqJ\nyzL3Pau2eeHVegUrdpL3ESlqjkpXc/8PZn6b7/OLwIeDQgbToiSMKolnKuScnAI9Ljl318bwTqeB\ne7K6KdSH5mzcXxU+FOt65ZjcAjefmD4hyZEjIZBMc5vNRlhYGLGxsZx++ukBfW5dXR2xsbFcccUV\nbN26ldmzZ/PEE08E3D55aDSvs7OTpUuXMm3aNM4888z951VxWIn/vDA0fDiYBGY0GkOSuDYWQkHi\nLpeLsrIyAIqKilCr1XR1dYW8YUmw3dHcbjcf/ridb2r6uWhmAlqljL+vbuCbahNTEqO5av5kwtS7\nd/irqpvpsDi468TsoJLPVqxrRqOQc96M5BF/JyVCy90nFfBDXQ8vrmvguo86uHl+FGf4UYa2qsFB\nWbebm45MRzUKIY4XcQY1fzw2i6T1LbyxtQOzU+SP3/QBkBAmZ3KMkimxKibHqsiLUqJWCIiSRJPZ\nR0WPm/IeDxU9Hip6vViHlOIdkxXGTQtiMWpGX8Q2tdrZ0OrgtgIP+iGPgc0LrzcoeKFGSb9HYEGy\nmqtnhFEQreC6z3qJVsPlk4K/954sl6OQwW0zZESrB7qmPbJVzTnbkrg4wcwNqSYMiuBKqMajwgEk\nCZ6uUpEaoebUKfuWEE4kAqkRH1S5wcDr9bJp0yaWLl1KcXExN954I0uWLOG+++4LaLyhBlcKhYKM\njAxWrVrFtm3beOCBBxAEYcI7mUmAdBBl7E8kDgkSh4EHpLq6GpPJREFBQUjD0KNBLpfj8QR21idJ\nEq2trdTX15OTk7Or3nRw3IloWBIoiXd0dFBVVcUb5TIitArmpYVz0/uVNPU5OXNqFqdMztwjTGxz\ne/i4pJYZSQZmpwT+XWxtMbOhqZ9Li9II14xeEy8IAkdkxTA9OYLHvqnioR96qehxc1Nx5Ige7V5R\n4rmN/aRFaDgmOyrgeY4EryjxbV0fGVE6Hjh1MvW9dqq6rFR2WdjWZeWr+oGyO7kAaUYF7TYfDs/A\n+qeUC2RE6liYFUGKUcvrm5qZHKfmrmPGzi2QJInn1/eQoJG4MH23Cl/VIePP2zX0umB+sorF08OY\nEjuw8fq+ycmWTg9/mebbg/QDQUkffNYi45p8gRjNwN/+tDSBIxMkniyR+HeNkc96w/hjeg+nRNsC\nMn/pcsvHrcJXdcopM8u477T9q8LhwFmupqSkkJKSQnFxMQDnnHPOHuVh40FTUxP9/f1MmTIFgJiY\nGK6++mo8Hs+urPr90ooUAWSHBr0dElcpSRIbN24kPj6e4uLi/d6sxOkcv3mF3W6npKQEvV4/bMQg\nVD3Fgx3T7XZTWlqKIAg4o7LZ2raDE3KjuP2TauQyOTcdNZPCxH2zez/eUYfN5eXK4tSAvw9Rkli+\nrom4MBWnFvqfFGdQK/jTCfm8urGR/2xvo6bXwwPHxAwbwv6kykZjv4c/H58a0lK1QXxV1UOb2cUf\nj8tFq5RTEG+gIN4ADCQEmuzunaRupdFkpyBJQ1a0jqxoPSkRWhQ78xfe2tKM3eNjcZF/G40fG+2U\ndrm4Z6obtXygpv/vZUpea1CSE6ng4WPC92h/6hMlnt5kJU0vcXZ68PfdP0rlGFVwRd6ef9NwlcCf\nZwqclS5x32aBm6vieLvTwV8zu8nUjq/T4HMtRjySwP/ljEOFVw+o8NOm7l8VDgeOxBMSEkhNTaWi\nooK8vDy++uorCgsLxzXGYAi9pqaGp59+mjvvvJOZM2fS2NjIk08+iUKhYMmSJQiCIJckaeKNMwQB\n6XCd+M8HgiAwZ86cMckiVJnZQzFexSyKIg0NDbS1tVFQUEBk5PAmE6E6vx6K8ZC4JEm0t7dTW1tL\nTk4O0TGxnPHMGvQqOf+t7CUrOpxrF04jSr/vGVinxc43VU0clxtDZnTgns/fVPVQ2+Pg97/IHneY\nWy4TuGxOOlnRep7+rparPmjnb8fGUBi7+6DX5RV5YXM/BXF65qWFPnLj8Yms3NxOdoyeOanDf8+R\nOhVz06OYmz4yOdtcXj7c0cbCND35sWOfOYqSxLIN3aTrJc5K8VFhFrh1i4Zqi8CFhTr+b5YB1V6R\niU9qHNT2eflHkY9gnWx/6hRY0yXjtukCYcrhn7cpUQKvHQNv1sCTJVrO2JbC7Wk9XJxg8UuVt7nk\nrOwI55cpHtL1/qvw0n4Z9x4AFQ6Bk3goSsyWLl3KxRdfjNvtJisrixUrVozr/YPr5vz58ykvL+f+\n++9n6tSpbN26lbS0NP785z8DsF8IfPek9ttHHUgcEiQOYzcNGSTbUJ+Rj4fEzWYzpaWlREdHM2/e\nvFGzxCeq/7c/JO5yuSgtLUWhUOyydl3xYwPVXQNtKI/NTeWcGTko5MPP/83NlSjlApeMYALjDxwe\nH69saCE7Rs8RWYHX8R6RFUOyUctDX1Xy2086uWV+JKfmDiyKb5da6bb7uPXopAmJ3vy3oodOq5tr\nF2QFNf4HJW1Y3T6unO2fCv+qxkqtycMjM9ysbFDwaLmKMLWMJ44zMi9532w1p1fiuS1WpkZKnJAU\nXCRUlOAfZXKSdHB+1hiNiQSBC7MFjk+RuGuDyP31MZTZ1Pw1qwe1bPR5/LM5AgSB67L9O8qSJHim\nWkVKhJrTpoy/hDAUCJTEQ9EhbMaMGWzYEFAnzD2gVqspKipi9erV3HvvvfzhD3/g73//e9Djjh8C\n0iGS2HZo5OAzfuvVUMEfEvf5fFRUVFBWVsbkyZPJyckZs8xrIsLpQ/t/D4dBO9oNGzaQkpLC1KlT\nUSqVONw+nv2uHkGAqxdM4YLZeSMSeElbD1tbujlvRiJRusDLWN7Z2k6P3cNV8zKCJtjMaD2PnDGF\n/DgDf/u+l3/81IvJ4ePlbWaKUsKZkhj6Tmgur8gbW9rJjzMwIzlwlW9xeviopI1fZOrJ9iNd3CtK\nrNjYw6QwkfebFTxYqmJOkppXT48elsAB3iq302kX+UOhL2hx83mrQGmfwPWThX3U/kiI0QgsXSjj\n2gKBd7oMXFqSSIdr5AW60ang3S4D56Z6SNL6t+lY3SmnpF/GNQvTUY5w7040AiFxm812ULQhHVw7\n3333XW6//XaOOuooduzYQXNzM4sXL6anp2f/TkhgoMTsQL32Iw4ZEh8LE2XKMta4vb29rF27Fo1G\nw9y5c/1+IPd3YpvT6WTTpk309fVRXFy8x+7/xZ8aMdk9XL9oOnPTRz6b9ooib26qIDFczZlBZP52\nWFy8u72dRVnR5MWFZgEzaJT85cQCTp+cyDtlVq78oB2bW+TyOYFHC0bDp+Xd9Ng9XDQ7JahNyPs7\n2nB6RK6Y5Z8K/6TCTIvFS4dTYJ1Jzi3FBh49JmLYbnAw0M70pe1WFsWJzI0JToV7RHiiTEGOEU5J\nG981ywSB6yfLeGy+jCqnmrN3pLDJMvym4+nmCOSCwLV+NnIZPAtPNqo5zQ873YnCgQynB4vBCKYk\nSTz00ENce+21FBYWsnLlShQKBZ999hkAgrC/GG7gTPxAvfYnDplw+ljY30rc4/FQUVGBy+UKqEPa\n/gqnD20Gk5+fv09jlS6Li2e/q2dWSizTkkcP662uaqbVbOfPx2cHpXZWrGtGJghcutPYJVSQywSu\nKE4n1qBm+Zp61HIBrxj6RFqnx8dbW9qZmhjOlMTAVXifw8PHpe0cMymMzMixVbjF5eOZtQPNSmL1\nch74RSSTIkfP6F++daCd6R8mB3+vvVU/YP369EIZ8gA3LsclC6SHybjxJ7isJJG/ZvZwXrxl189r\n7Eo+7Arj8kw3sRr/vrtvuwZU+D2nph0wFQ4HLrEtFFi/fj2ZmZmcffbZ+/zsX//6FzCg1iVJCm34\ncBRIh81efl4YS+3sTyXe3t5OTU0NmZmZJCYmBqTE9kdim8PhoKSkBJ1ON2JN/RNf1+D2iZw9I2fU\nsS0uNx/uqGVGcjhzg0gS295m4Yc6ExfMTCFGH1qzm0HU9diQywS0KiW3fVTJbxemcXxu6PyzPyrt\nos/p5bZZqUGN85/trXh8Ir+eObYKb+xzc9MnLTi8EkelqblnUQQaxej3XZPZy9sVdn6ZJpIbpC2/\nxQPPVMgpioVFgbvrApBjFHj9GBm3r5X4a20MpTYVd2b0oJLB0uYINAq4Kst/Fb60UkmyUc3pByAj\nfSj+l0m8pqaG//znP2RkZFBQUEBycjIqlWqXMKqpqaGjo4OLLrooVpKk4JvPjwVBONzF7FDD/lDi\nTqeTsrIy5HI5c+bMCcraUC6X43IF18N5uDFFUUSSJJqammhubiY/P5+oqOFJorzdwjubWzkmN404\nw+hZ5h9sq8Xh8bJ4XuAlZT5RYtmaRmLDVJw5NXHsNwSAuh4bq6q6OD4/nRMLM1j2w3Ye/7aBqi4b\nV89LCVqp2d0+3t7WwcxkI/nxgS++vXY3n5W1c3y2gbRRupZIksRnVRYe+6ELl0+iIFrBQ0f711bz\nqY0WlDL4XX7wm9sXqmSY3HDLNFlIkgSNKoGnj4And8DyinAq7Wp+l9LLZz1hXJftJsrP/d1XHXJK\nzXLuPe3AnYUPwufz7dGhzB8cLCR+/vnnY7Va2bZtG9u2bUOlUiEIAmazmR07dpCVlcUdd9zBfiFw\ndpq9HCbxQwsTpcQHw95NTU00NjaSm5sbkmzSiaoTdzgcrF+/nvDw8FHbmkqSxJLPq9CplJw2JXPU\ncZtMFr6taeaUgjjSI7W73t9ldVNvctBgciAAkxMMZMfoRlxMv6zsprbHwR+OykatmJgH9OX1jehU\nCk6enIlepeSGo2by3tZqPi5roK7XwR3HZhGlG99COxTvbe/A4vJx4ezgVPg7W1vwSRKXj6LCbW6R\nf/zQyZc1VqJ0Ktx2N39e6F8UZHOHm1WNLq7P9+FH1dqoaLXDy7VyTk0TmBwZuix/uSDw+6kC+REi\nf9mg5tryBHRyiV/72U5VlOCpKhXxOuGAq3AIXImHonthsPjqq69YvHgx7e3tuwSAx+MhOTmZhQsX\nHpA5SRwuMftZ4UBlp9vtdux2O1arNaQ2r6EmcUmS6O3tpa+vjxkzZhARETHq739b1cNPtb1cMCsX\nvWpkUpMkidc2lKNRyInSKVn6XT0NvQ4a+5w4PPtumtQKGflxeqYmGpiSaCA3Vo9SLsPm9vLyhmYK\n4sNYmDkxrSE3N/extbWfc2fuvia5TMY5M3NJjwrn5XUl3Pifcu48NpOC+PEnE/U7PLy3o5P5GVFk\nxwSejNRhcfJFRSen5oaTPELXkrIuJ/d+3UG71cNpk5P5rKyVUyZpyR7jDBwG6sifXG8mXgu/DoG9\n6tIyOZIEN0yemEX15FQZbp/InzeAV4TP2xScmzb2s/x5m5xKi4xrp6kOSF343giExO12e8Ae56HE\nrbfeynfffcfDDz/MkiVLmDNnzgGekYB02LHt0EIw9qjDQRRF6urq6OzsRKPRUFBQELKxIbSRA6vV\nSklJCQqFgrS0tDEJ3OMTefDzSuINOn6RnTLi73Va7Lzw0w5qewasQ1/e0EKYWkmyMYx5GVEkRYSR\nbAwjyajHJ0pUdpmo6jRR2Wni3xtbAVDJBfLjwvD4RCxOH1eekDkhNds+UeLl9Y3EhGk5KmdflTwn\nPYHEcD3//H4Lf/y4iusWpHJyfsy4PuONrR24vCIXBanCV25qRibAZcOocFGSeGN7H88Swo40AAAg\nAElEQVRv6CFSq+auk6fxZUUbcgGunenfxuGLOielPV4emOlFG+QKUdoHHzbLuCJPIEk/MUQpSRLv\n1UtEamRMipBz1w7Y1ifjz5MH3OiGg1ccUOGTojUsSAk8shJKBELikiQdFK0/p0+fzn333ccrr7xC\nZGQk6enp6HQ6jEYjWq2WBQsW7N/e4sJh7/SfHfxR4g6HIySf1d/fT2lpKXFxcRQXF7NmzZqQjDsU\noVDioihSX19PR0cHhYWFOBwOv/oIv7mxhbpuO79dNG3YenCL081HJXWsqmxCBAxqJVfMm0JapAGD\nRjXidzE7NZ7ZqQNhTavLTVVXH5WdJkraumk32xGA9Y29pERoR+3MFQhWVXfRYLJz9YKpI4bzUyIN\n3HnCPJb9tJ2nvm+kqsvGdfNT/XKL67S4+KS0i6NzYkk2jq8SYSgaTHa+renm/KkRxO5lYN5r9/K3\n1Z2sb7EzNz2aaxbk0GNz8n1NF5dM0ROvH3uxd/kk/rnJQoFR4ozU4bO7zR7QyhnTuU2S4JGSAXvV\nxfkTt6B+3w4bu+GWYj2/ytXx/BYrK7bbKLPIeWKWk+RhasU/blVQZ5Pxm0lenA4v7e3tGI1GNBrN\nfrVlHorxkvh+sSD3E3/605949dVX0ev1bN++nfXr12Oz2XA4HJhMJjZt2jTuCpxgIHHYdvWQQyiU\nrdfrpbq6GrPZzNSpUye0fjPY+VosFkpKSoiOjqa4uBiZTIbL5RpzY2B2eFj6TS15cZFM36ukzOX1\n8UV5A5+XNeD2icQZwmm3mPnNohlkx46u7vdGmFrFzJQ4ZiTH8niflT6Hi/y4KN7c0sLq6m6umpdB\nUZp/CVpjweX18fqmJrKiwylKG/1sVK9W8rsjZ/L+9ho+La1jS4uFxfNSmJ9uHHXxf3VTGwhw/oyR\nIxf+4PWNTehUMi6avvvaRUni61orT63pxuaWWDx/EsfmJiAIAku/rcegknHZFP9Crm+U2mizidxW\n5GOrSaDRCo02YderyS7Q7wadAoqiRebHSiyIFZlk2Nfl8tsOgXXdMu6YIWAYwV41WIiSxBMlEskG\nOWfl6JDLBK6bZaAwRsnd3/dz7g86/j7dwYLY3fe1RxxwZyuI13PpUblUVVXhcrmoqqrC4XDsUpBG\noxGDwbDfFGQgShzGFij7Azk5Odx9992cffbZTJ069UBPBzhcYnbIIdgz8e7ubioqKkhNTSUvL2+P\nB2toa75QIdA68aFh/smTJ++RFDOWYxvAU6tq6bN7uH5Rzq5r9IkiP9S28cGOGvodbvLj4pmVksYb\nmzcwPzNx3AQ+FJuaOynr6OXcmfkcnZNGRWcvb24q429fVlCUGslV89KJNwSXefXhjnZ67R6uWjDd\nrwVRJhP45fRsCuKjWLmpnAe+HOjGdu38FNIi91Ubjab/Z++84+M6q/T/vdP7jHqXrN6sYkmW3OP0\nHkhCIBAILJCwC+yGpS77W5aFpWYDS1h2ScISSgKbBJKA05sTO+6WZVu99y6NNL3P3N8fihXLVhnN\nyIkT+/l89IctzXvvSHfe5z3nPOc5bnZ3z3BDaQrxusjb4jom7RwZnOUz1bHzY0aPDrt48KiZLrOX\ndbFa/vmqAjJi5gi7eczCyREL/1Cjx6Bc/tkLhESe7nDxy+MOpAL8Y/3bW4NEgGStlHSDjMuTZKTq\npYw6ghwd9bK3OQBISVDB5vgQmxLmiD1WCfe1SsnSwW0r2KtGgxeHRDosIt/drlswiW5Hporf3iDj\nn163cHe9mn/I93FXrh9BgL8MyxhyCfz3DesAUKlUZGVlAXPRrdvtxmq1MjY2RmdnJxKJZJ7UjUZj\nVF0ly2G1JB4Khc4LAj8d5wuBg0BIuBiJv69wrvrEfT4f7e3tBAIBqqurFx16f2rttSTxSPrEbTYb\nLS0t82n+M+9npRR9z5STR48Msz03jczYOfJvHp3mieNdjNmcZJhM3FpeTYYphkfrD6OQSbm1Yvn+\n8eXgDQT5U0MH6SYdO3LnItjCxFi+eeVmXu8a5PnWHu55qpFbKlL54PrUiGZ9W9w+nmoaoTI9gfyE\n1UX2RcmxfOuaTezpHmZXUw9feKqNG0oS+FhVCnrl2x+t39ePopRJuKU8cvc3URT5w7EhYtRSPrTe\nRPuUhwePmmkYdZOgU/LF7QVsyUmYH/caEkX+WN9HslbKh4qWbv8LhERe7vPwm0Yng7a5Q+w1OWpK\nEhSk62WkG2Qka6VLjmodcwSoH/NydNTLm2Nedg3PPT/xSpj2wr21AvJzJBrzh0T+qwXyY2RcmX32\n5y7TIOPX18Xy/QM2ftYJjVYJ31nv5Zc9CspT9WzPi8Vmsy0gTkEQ0Gg0aDQaUlLm2hj9fj82mw2r\n1TqvutbpdPOkrtVq14RMV0viTqfzvBC1nZcQBMTznMQFQTAB/wusZ64r7tOiKB5c7ToXDImvhNVG\n4qIoMjY2Rl9fH7m5uSQlJS35QT5F4qvtAV0OqyHxUChET08PZrOZ9evXL9lXuhyJi6LI91/oQCmV\n8sHyXAKhEH852cNL7QPEa7V8ZEM1RYlzv4OW8TF6zGZury7EoI488nyhtY8Zl5dP1ZUjPe3AIZNK\nuLJoHTWZyTx5soPHGobnU+xV6auL+v94bBh/UIz4sCGVSLisIJONWcnsauzhmZZh3uiZ5c6aVK4q\niKNr2sXBASu3V6WvOO98OZwctdI8ZuMTlTHcu3eS1/scGFQyPlmbwxWFyWfV8Q/1TdNrdvLtbUaU\nixDwKfJ+uNHBkC1IqkGJQIDbirX8Y134v8MUnYwb82XcmK8lJIr0zAZ4c9DNbxrnXNR+2iSilIlc\nlrr2RP5kn8iwU+Q/N+kXzKo/HWq5hH/fYWR9gpyf19v5wJtSZnwC3715XdgZMrlcTlxc3LxbYSgU\nwul0YrVaGRgYwOl0olAo5kndYDBE1IUiiuKqDvrni+Xq+QiR94Sw7X7gRVEUPyQIggKIaKTjRRJ/\nC6uJxN1uN62trSiVyvkpXmu1drgIN51+SmSXnJxMbW3tspvEcgeD3R3T7O+Z4SMbCgiGRH6yu4Hu\nKQs1GZlcXVSC/K0IwhcI8HJ7Kxkm3bLK9ZUwYXfycls/tVkp5C0RIcdoVHx2cwVt2WaeON7G915u\n5+qiRD5dty4s444+s5PXOie5ojCTJEN0EY1eqeCOjcXsyEvnsWPt/GLfIM+3ToIgYFTJuLE0cnMa\nUZxTzqvlAn84OYtCKuGWigxuKE1Dozj7I+wLhPi/hj4KYmVcfUaEGgiJvNjr5jeNTobtQXLi1Pzz\n5SnsapnE5fPzmcrIe44lgkB+rJwXe1wEQ/CN7fH8qdnKPQf8XJIC/1wpWTOFuisg8kAbbEiSszlt\n+fS2IAjcXqJlnVHGV3fPsiFdz6Z1cweVSMpcEokEvV6PXq8nPX3uGfd6vVitVsxmM729vYiiiMFg\nmCf2cyGYu0jiy+N8TqcLgmAEdgCfAhBF0QeEN/j+DFwwJL4WfeKiKDI4OMjIyAiFhYVn+YgvhXd6\nWAnMpea6u7uxWCyUl5eHlXZbak1fIMQPX+wk1aAl2aDl3186jMcf5JbySspT0xb87N6ebqweD5/b\ntnFB9LwaiKLI48c6kEkl3FxesOLPFyfH8c9XbeHZ5m5eap/rQ//aZfnELDMlTRRFHj7cj1Yp5/r1\nORHd52LIiNHz1ctrqB+c4LFj7di9flQyCffv6aYgQUdhop7ceC0q+dIbjCiKTNi99M046TO7aBie\npX9mTp1/ZVEKt5RnYFrmvb3QNsqUw8e/XRWD9K1UdiAk8kKPm980ORl5i7y/dWUqtZlG9vdbaB53\n8LVNphVr5ythyBbgiTYH1xXouKFAzzV5Ov7UYuPhhlk+8HKIvy0WuLMg+hT7H7pEzB6RH1+qD5sc\n22f8+EPw5cvfHv26VmUupVJJYmIiiYmJ8+va7XasVus5E8ydL25t5yeE813Ylg1MAb8RBKECOAbc\nI4qic7ULXTAkvhJWmjdut9tpbW3FZDIt62S2GM4ViS91v7Ozs7S1tZGamkptbW3Ym9xSJP7bg4MM\nzbrZvC6Zn+85TrxOxydqqkjQLdxAph0ODg70Ri1mOzkyRfOYmVsrCjCGmY6XSyXcXFFAZqyBR440\n87VdzXzj8gLyExaPVA4PzNIybudjNUVoljGriQSCIFCdkcTzLX2IIhQlx9M/Y+XI4CwwJxTLitFQ\nmKinMFFHikHFsNVNn9lFn9lJ/4wL11tGOAJzQjqtQsp3r68gzbh8xs3q9vHXxiG2pyupSZn73Y3a\nA/zrm1aapvzkxmn41pUp1GbOqem9gRC/OTxMXoycDxRElM1bgJ8ftSKXCtxVPZc9kUkEPlpm5LJs\nLfcfMvOzZhfPDMK/bICahMiI3OIVebhTZEeGkrLE8ERmNm+IR5udXJIfS2X62651oVDonPRZS6VS\nTCbTvOdCOIK51eJiJL40RCD07pJ4vCAIpw9of0gUxYdO+7cMqAL+XhTFw4Ig3A/8E/Ct1V7ogiJx\nQRBW3Vt5qp48PT19lpo7XJwrS9czEQwG6ezsxOFwUFlZiUazuk15MRKftHv5nz196JVyDvaPU5aS\nyg2lZSjPqPmJoshzbc0opdGJ2XyBIE8c7yTFoGVn/uqnlFVnJJOk1/Lg/uP8y/Mt3L05m8sLFo6X\n9AdD/PbIAGlGLdtz05ZYKTocHhhjxOrgU3XlVGfOpdIdXh/9M1b6zRb6zBZe757mxfaJ+dcopBJS\nTXqqMlNJN+lJNxnoM1t48kQ7n99esCKBA/z5xCDeQJAv1sTM+ab3erj3sA1BkPCVnevYmRu74FD3\nl6YJJhw+vnV1/HzUHimOjHrYN+ThczUxxGkWPh9JOhk/uCKJ/YMufnbQzN/sCfCBLIEvlwvEKld3\n3QfbRFwB+LswzWsAHml24vCJ/MPOhRbBa901shRWEswNDQ3hdDppbW0NWzBnt9svkvhSEN71SHxa\nFMWaZb4/DAyLonj4rX//mTkSXzUuKBJfLU5FtCkpKYuqucPFO0HiMzMztLe3k56eTlFRUUT1t8VI\n/P/9tRW3P4hECHJDyXqqMzIXXbtxbIQ+s5mP1RRFLWabdri555LqiNPx6SY937hiE78+2Mh/7+ul\nb8bFp2ozkb213jMtY0w6vHxpZ2nE11gOvkCQvzZ2kxVrYEPG2yO7dEoF61MSWJ8y118fEkXGbQ6m\nHC6S9FoS9doFAi2PP8CD+45RnGSgKn3lSWXDFhevdY5zS4GGOLWEb+218kq/h9JkHV+5ZB2J+oV/\nl2mnjz+dHGdnlorqlOgmwgVCIvcfsZGil3Fb6dIH3a2ZGqpSVPzuhIXHmqzsGYd7a2FzUnjP65BD\n5LFekRvz1OSEYSELMOUK8nibi+vXJ1KQuLCs9E6R+GI4XTAXCAQ4efIkGRkZWK1W+vv7cblcywrm\nLqbTl8f5XBMXRXFcEIQhQRAKRVHsAC4HWiNZ6yKJnwFRFOcjWqfTGVFEeybOJYkHAgE6OztxuVwR\nzSU/HWeS+PEhC3u7zChlMj65cROpS6T8XD4fr7S3kRNnYEcUYrYxm5MX3xKzFSZF54+uUyr44o4q\n/tLYxfOtAwzMOPnKpQWIosiTJ0cpT42nJOXceLDv7hxkxuXl4xvLl1RNw5wQLNWoJ9W4+Ea8u7Mf\nu9fPx2pKwjqU/eFoHxq5QF2qgjt2mZl2BbmzJpVby5MXjbJ/d3SEkCjyxZrIR8Oewq5OF70WP/9+\nWeKKbnpquYS/3RjL1Xk6vv36JH+7z8+XywTuzBdWfJ/3N4vIJAJ3V4YfgT580kFQhM/vyDrre8Fg\ncM3mGUSDU/dxpmDO4/Fgs9mYnp6mt7cXAJ1Ox/79+7FarcTERG94FAwGqampIS0tjWeffTbq9c4H\niO+NPvG/B/7wljK9F/ibSBZ595/edxArpdMFQWBycpLu7m6ysrIoLi5eE0XpuSLxQCDA4cOH1+xe\nTyfxYEjkO892oFcq+cymrZiWORy82tmOy+/njo1Vy5LWchBFkT8cbUMpk3JLxcpitnAglUi4tbKQ\n9Bg9f6xv5eu7msiJ0+ILhrhtw9pc40zYvT5eaO1jfUo8+YkrR89Lwebxsruzn7qsOPITVo62Gkdn\nOT4yS02ynK+/biHFoOTeG/MpTFxc0Ng+6eD17hk+Wa4jTR/dNmD3hvjVCRuVySouWRf+gTc7RsED\nN6TygzenuK/RRbsFvl0NqiV60hvNIi8Ni3ymQku8JrwNetAW4K9dbj5cnUrGIkY856omvlos1SOu\nUqlQqVQLBHPT09P09fWxd+9epqenefPNN9myZQvXXnstRUVFq772/fffT3FxMTabLer3cT7hfJ9i\nJoriCWC5lHtYOK/le+8kvF4vbrebkZERampqSE9PX7OWkLUmcb/fT3NzMz6fj6qqqjW719Md2x6r\nH6Zt3M7VRSXLEvjg7AwNw0NcXpBBRkzkqb3D/eN0Ts5y0/p8DKroUrtnoi4rla9cVosvCEcGZylK\nio26pWwpPN/ShycQ5KaywqjWeaG1h0AwxO3V61b82VBI5LeHepBLoH7cz5UFcdx/c/GSBB4MiTyw\nf5B4jYRPlEWfjv1Nox2rJ8Tf18Wu+jnUKCR897JEPltl4tlBkTtfFxlznX3QFkWR+5pCxKol3FEa\n/t/uoeMO5DIJd29dXF/xbqbTT0e4Ri9SqZSkpCS+973vcc011/DTn/6U733ve5hMJgYGBlZ93eHh\nYZ577jk++9nPRnLb5zVCSN61r3cSF1QkvhhEUWR0dJT+/n7UajVFRUUolWtLIlKpFI/HsyZrTU1N\n0dnZSXZ2Nna7fU0tIE9twGaHj/98tYecuDhKk5fubw6GQjzX2kSsRsmNZbkRX9fp8/On4x1kxxrZ\nlhudt/hSyDDpidWocHj9tIyZefxYB7duyJ+vk68Fphwu3ugaYtO6NFKM0YwadXKgd5grCpNJMSxf\nHhFFkQcPdDFq86CUCXzz0my2Zi+fYn25Y5pus5vv7IhBu9IUkxXQb/HzRKuD6wt0FMRH9rmRCAKf\n3BBDXpyS774xyUdeE/nppoXq9dfH4Pg0fGOTLux77pzx80q/h7u2ZhCvW/xz8l4j8dPhcDgwGo0U\nFhZSWBjZofFLX/oS9957L3a7PaLXn78QEC+QGPXCeJdv4cwoweVyUV9fj9Vqpa6uDq1We07S3msR\nifv9fhobGxkeHqampobU1NSIrFfDwX2vduHyB7m2eP2ykdXB/j4m7A5ury5CJX/7POgPBhmatdMw\nNMGY1bFiR8DTJ7tw+PzcXl0ccTp+JRwZHKN/xsZ1xaXUZWXzWucgP9t9DJsnIn+FRfGXk91IBYHr\nS/OiWueZpk4UMgm3Viw/stTpDfCT19vY0z2JRi7hgQ+VrkjgNk+A39ePsCFJwZXZ0U2VEkWRnx62\nopFLuLsm8tLBKWzN1PDQTanoVDLu2hvisZ4QoijiD4n8Z5PIOqOMm/LDv+f/abBjUEn51Kalf4+R\nDh1Za0RK4tEI25599lkSExOprq6OeI3zFSIXI/H3NUKhEAMDA4yNjVFcXDwvDol2CMpSiJbEJycn\n6erqIicnh+Tk5HliPRd2rl2zQZ46PsbW7FwSlmlfmXW52NPTSUFiDL5AkL80djNqdTBmdTLpcHE6\nbxtUCgoSYyhMiqUwMYYkvWb+PfRMW9jbPcJlBVlkxETuFrYc3P4AT5/sJM1opCp9Tl2fajDwTEsT\n33/pEH+3rYJ1cdGJu/rNVo4OTnBNcQ5GdeQDWfrMFk6OTHLbhkyM6qWzLB2TNn6xp4MppxeA716b\nT0IYw1UeqR/B5QvylU1xUZdg9gx6ODrm5Z5NscSo14YIs0wKHrople++Mcn3j7tpt0C+AfrtIv9x\nqQ5ZmG1w9WNeDo74+PJl2RhUS29z7/VIPJoWs/3797Nr1y6ef/75eQHdxz/+cR599NGI1zyfcL7X\nxNcKFxyJ22w2WltbiYuLY9OmTQs+wOdKgBbNcJW2tjZEUWTjxo1npc7XYqb46QgEQzzS5seoUrEj\nd+locmDGzGPHj+EPhuicnKVzchaJIBCn1ZCgNVCUmEqiXk+MWsOE3UbfjJnOSTP1g3M90Ua1gsLE\nWPITTOzuHCRGreSG0sjT8SvhhdYebB4fH67YOE9c5anpJOj0PHHiGPe+Ws/HNxazJSeyASWiKPJ4\nQwd6pYLLC7NXfsEy6zx9sh2TWs71JYv3r4dCIk83DfHkiUEMKiVSQeDS/FiKElfezLunnbzYPs2H\nS7TkhtmetRQ8gRD3H7WSEyPng8Vre/jSKST86Mokfn1slt+ftCIToDRezvaM8NL1IVHkv445SDEo\n+NjG5X0A3ssk7nQ6I/KtOIUf/vCH/PCHPwTgjTfe4L777nvfEDgIhMR3/+/6TuCCIvFTA0tKS0sX\nTUOdT5H4+Pg4PT095OXlkZS0+IzrtT50PFY/wpA9xG2VJWeZuQBMOey81tlB++QcGefExVGdkUmi\nTkecRotskU0o3WSiOiMTURSZcbnoM5vpmzHTNm7myMA4AEWJsQTOQVkAYNzm5PXOQSrT0kkzLXSR\nSzEYuWvTNv7c2MBvD7cwMGPjtqqCVdfJjw1N0jNt5fbqkgVlhdXi+PAEfWYrn9uat6gt67TTy3/v\n7aBtwkZ1RgpOnw9vYJZP1qxsWBMSRR7YP0SMWsJno/BHP4VHmhyMO4L8/LqEsKPj1UAiCNxVE0u/\nxc/eARdD9gAnJv1sSFpZA/JKn4d2s58f3FS4Yrvbe5nEL/aJL41T6fQLARcUiScmJpKQkLDitLG1\nxmrW9Xq9tLa2IpVKF42+T8daRuLTDi//+VoPuXHxlCQlL/ie1ePmje4uTgwPIZNIkEskJOh03Lmx\nLuwatiAIxGm1xGm11GRmMuN08t/79qJTKumYnOE7L+zng+X5bM5OW7O6uCiK/Ol4O3KplCvyF2+9\n0SgUfLyqlle7Oni9q5dhi53PbS0P27DGHwzy1IlO0ow6NmdHLsrzB4PsauogK1bLJblnH9qODEzz\n4P5uAiGRj9WUoVMoeOjAMf6mNo0YzcpR9WtdZtqnnHxrWww6xdubmyiKzHpCjNqDzHqCFMUrSFih\nfWvUHuDRZgdX5GjZkBJdXX05jNv9HBp2szHDwKjNyxdemuEfavR8pFiz5GfYFxT55XEHRUlarl+f\nuOjPnI7zqSa+2rKY0+lcM8e2nTt3snPnzjVZ63zBxXT6+xArRdrvZiR++mjT/Pz8+b7QaNcNFz9+\nqQu3P8i1JaXzG6Tb72dfbw+HB/oQRZH1iVm4/F76LBN8sKwiqp7wZ1qbkQgCd27cjMfv54W2Zv5Q\n38rBvhE+UlW8JvXxk6NTtE2YuaaoBO0yHQcSiYSrCotJNRjZ1XKS7710mA9XFVKdkbhi3fi1jkGm\nnR6+uKMmqsPHnq5BzE4Pf7t1PZLTIltvIMgjR/t4tWOcjBgDn9hYQaxGzX+8tp9Ug5KbSld+Tmwe\nPw8fHmadUYbbH+TnR62M2gOM2IOMOAK4/QuFhzkmObWpCmpTVWxIVqA6I5q9/6gVqQCfr41ezLYc\nHqifRRDgC1sz0Sik/HRPP/951ErLtJ9/3mxAvYhK/cl2F2OOIN+5KSesv8d7ORJfaz3M+wkiAsGL\n6fT3H1bakKVSKT7f2qmVT193ObL1eDy0traiUCjCGm16CmsViR/oMbOrcZxLcvOJ1+oIhkIcGuhj\nX28PHr+fvNhUNqbkYfW6eK67nh25eSRHUYtrHB2hZ3qaa4pKMarUGFVqPrlxM42jI7za1caPXj3E\nJXmZ3FiaizrC4SS+QJA/H28nUadjY8bZTl2LYX1KKvFaHX9tPsFD+xspSIzh9upC0k2Lpyxtbi/P\nt/axPiUhKoc5u8fLy+09VGfEUpZ6akSmyL6+Kf50fIAph5fLCrK5tmSuJW5Pdz8TdiffujJ32ZGr\nwZDI/r5Z/ufAIA5vELsX7jtsQyEVSNIrSNGrKUlVkqJXkmxQolNIaZ1wcHzEzpMdDh5rdSKXCJQl\nyqlLVVGbqmTWE2Tv4Jw/eoL23G0fTRMeXut1cvuGZBLeag/7f1fk8KeTEzxSP0qPJcCPd5rIMLx9\nDzZviIcbnWzJiWHzCir9U3ivkvhqZ0BciLgYiV+AOFeR+FJkK4oiIyMjDAwMUFhYSHx8/KrWXYtI\n3OsP8u1n2onTatiWk4vV7ebPJxsYsljIMMRTl1tAnMaAPxjg2e6jxGu1XLKM6G0lOH0+XmxvJd1o\nouY0chUEgYq0dAoSk3i9q509XYM0DI1zS0UhGzOTV62kfqWjnxmXhztrVud5n2wwcNfm7TQMD/J6\nVwf//uIhduZlcFNZLlrlwgPFX5t68AdC3FwRnbHL8609+AIh7qhZhyiKHBua4fGGAYYsLjJMBr6w\nvZy8hLlDgsPr46W2bqrSDdRmLq6oD4ZE9vbM8PiJcYatc/4EZck6Pl6TSrJeQaxGvmSUWpKs40MV\nyXgCIVrHHTSM2DgxYueXDTZ+2TA3gc2glPCBonNXiw2JIv91yEysWsaHyt8uLUgEgY9UJpMfr+He\n1/v41HMzfGebgW0Zc90Av292YveF+PJlqxMXrvWc70gQaVr/fLj38xIiF4VtFyLOVU18sQ+a2+2m\npaUFjUZDXV1dRP7NaxGJP/BmP4Ozbj5RU0f/jJmnGk8QDIW4fF0FebFvG73Uj3Vj87r5dOUm5FHU\nEF9sa8XjD3BD9eK+4mq5nOtKyqhMy+CF9mZ+e7iJg30j/M2msrCd3CbtLl5q62N9cgrZcas7GMEc\nWdRkZFGalMLr3Z280TXA0cFxPlCWy/bcdCQSgWGLnX29I1ySl0miPnL3tzGrg/29Q1xdlILV7eeX\n+7romrKToNPwydpKytOSFvyenm/pxBsIcFfd2S59gZDIG91mHj8xzpjNS5pRQ4JORSAY4FtX5aJV\nhP93U8kkVKUbqEqfy7jMuPw8eHCIfX0WbN4Qd+0a4ytb4tiYtvY18Vd7nLRN++lyz6cAACAASURB\nVPjSjizUiwj8qtIN3P/BIr7/ai9f2W3h0+VabshT83ibkxvLkyhMeu9N9roYia81BETxwjjgXFAk\nvtKp9VxF4qdDFEWGhoYYGhqiqKiIuLjI07DRHjp6ppw89GY/ZSmp9M+YebO3m1i1jiuzN2BSvU1M\nk04rTZP91GRksi428vvtnpri5OgI23PySFxBVZtqNPE3tVtpGB7klc5WfvzKIe7eWklW7PL93KIo\n8kRDGzKJhKuKSiK+VwC1QsF1b01ue7G9hT/Ut7O3e5iPVBXyXEsfarmMa0qia437S2M7KpmU4VkX\nL7Y1YVQr+fCGUmqz0s6asDY4a+VQ/zA3liYu8AH3B0O81mXmTyfHmbD7yIrR8fc7CphxefhDfRdf\nu3Tdqgh8MfiDIY4O2ti8LoZrihJ58EA/X35xnCtytHyxLvas0aORwhMI8UD9LHlxai7PX7rmnqRX\n8h83FvI/+wd5uHGGXV1uRFHgc5sjaxN8t7FaEne73VEPZno/Q+RiJH5B4lyPDHW5XLS0tKDT6SKO\nvk9HNJG4KIp8+5k2ZFIpFreLprFRiuLS2ZpRjEzy9mYSFEO8OdiETqnkqsLVD1c4BV8gwLOtTcRr\ntWzPDi8dfyoiTjOaeOJEPT/ZfYSP1ZSyad3SG/Xx4Qla3xKz6ZWRm66cjiS9gTtrNtE6Mc4rHa3c\nt/sYAJVpScy6PKhkslWPNPUGAuzvGaJ13AxA74yTG9cXsi03E8Uim3lIFHnqZCsmtYw7qufevyiK\n7O6a4dFjo0w5fWTH6bnnkiIq0uKweXz87zOtVKbquSQn+klXDx4cRhDg03WZJOiU/OzmMp5sHOXJ\nk2McGnZzd3UMNxXpo55J/liTlSlngK/uzF5RmKaUSfjSjixiNXKeODnBzUU6pge7GO8NoNfrMZlM\nGI1G1Gr1eZ92Xi2J2+12tNpz4///fkHwYiR+4eFcReKiKOLz+Thx4sQCh7hoIZVK8Xq9Eb326RNj\nHB2woJRJGbfZuTSrjIK4s/uNT4z3Mu128NGqalRRKGF3d3cy43LzyZpNi/aTL4cUg5HPbtrGkycb\n+P2RZoZnbdxcUXAWcXr8Af58ooMUgyFsMVu4EASB0uQUcuLi+a+9u/EEApwYmeDEyARKmZSsWCM5\ncSay402sizWheUuQJ4oisy4PI1Y7I5ZTXzamnO75tS/Lz+aKwpxlRXxHBkYYmLHy5UvmomqrJ8B/\nvTnAoQELOfEGPlFbzPqUtweQPNbQRSAY4vNbM6ImsEMDFg4PWvlUbca8K5xCJuGjVensyI3jwQMD\n/PSgmee7HHx1axyFEXqoTzsD/KHRytZ1JtanhF9zb5twYlLL+Nr15ehVMkKhEHa7HavVSnd393zU\najQaMZlM6HS680LMdjpWS+JOp/Nij/gyEBEuCtvejwhHnb7WkbjT6aSlpYVQKMTGjRvXtCUk0kjc\n7PDynWfbAVBLlVyZv4FY9dkbgtlt5/h4D2UpKRSf0Tu+GgxZZjnY10d1eiZZEabjtQold1TX8Wpn\nG7u7+hmxOvjM5nJ0yrf76J9r6cHq9nJrefU526QbhgdxBwJ8qGwj8RodI7ZZRqyzjNhmeWmyl1OV\nymSDFq1CzqjVgdv/9sEwRq0hQWtEr9TROzPFx6rL2Ji1vFmL0+fjuZYOSpJ0XJoXy7EhKz/bO4Dd\nG+D2qjyuLMpYELW2jM1wqH+Sj25IJs0YXTbCEwjx4MFhMmPU3FB6dv96mlHNd64pZG+vmd8cHuTu\nXaPcWmLgM1UxaBWr+xs8UD9LMAR/U7uyec0pHByw0jTu4F+uyUP/lr2qRCLBaDRiNBrJzJwzGnK7\n3VgsFkZGRrDb7chkMoxGI4FAgEAg8K7PFBdFcVXPrN1uv0jiK+BiOv19iuVmiq8liYuiSH9/P2Nj\nY5SUlNDZ2bkm656OSO/3O8914AmEyDDEc2V2JXLp2Y9BUAyxZ6AJlVzOdSXrI77HQDDIX5saMahU\nXFEQeToe5uaDX11USrLeyHNtjfzolUN8bmslGTEGhi12Xu8apCo9k3TT2mQ6zoTd42FvTxd5cYnk\nxs31ZxvVGkqS5kjHFwgwZrfME7vHF6AwPpVEnYEEnZ4ErQGlTIbL5+VXR96gMDGOmsyVa7gvtHbj\n8vn5TF0ODx0c4pnWKdKMWr50aSWZZ4x/9QdDPFrfQYpByYcrIj94ncLjx8eYdPj4/vXFSzrZCYLA\nJbnxVKeb+MOxYf7cMsn+QRc/uCKJ3Njwpuw1TXh4qdvBhyuSSDGEa7QT4uEjI+TEa7h1w9LT9gRB\nQKPRoNFoSE2d+337fD5mZ2cZGxvjxIkTiKI4T/xGoxGVam1KMecKF9PpK0CE0AWi/bvgSHw5rFXd\nzOFw0NLSQmxs7Lw/+7kYVhJJJL6v28xLrZOUxGewLaNkyfd8cqKPKZeNj1RWoY1i3Omenm4mHQ4+\numEjStnavPeKtHTidTr+dKKe+3Yf4eM1JezpHkItl3F5fnTtXsvh1a52gmKIy/IWF8wpZDKyYuLJ\nilleEf9mXye+YJAPlhev+MwNzVo50DvI9pwYfrZ3gCGLhysL07ltQ+6iXQIvtA4wbnPz3WvyUKxg\nOboSBmfdPNU0yaX58ZQmrxz16ZQyPrdlHTty4/iP3d383TOj/POOBHZmL082IVHk/kNm4jRyPlwZ\n/sHj2dYpxmxefnn7+lVbvyoUCmJjY9FqtWzYsIFgMIjNZsNisTA2NobP50Or1c7X1bVa7XlVV79o\nubo8LgrbLiIihEIh+vr6mJycpLS0dMFwgnORql/tmk5vgG/tasOk0rA5vWjJTWnGbadhrJvS5GRK\nU5aOcFbCmNXKm709VKSmk5+wsrPYapBmNPHZTdv588lj/OZwMwA3lZajXsP56qdjaHaGxtERNmXm\nEqOOPAKasFs5OTbI9twskg3Lt0KFRJEnT7ailEnY3zeLTqXgK5dVsD5l8ZLEuM3Fsy39bM82UZ0e\nneOdKIr88sAQSpmET25cfiTqmShO0nPfTaX8+LUuvrV7kk9Wmvh0lWlJodrznQ46pn18bee6RVvK\nFoPNE+Cx4+NszYlhW25kznGnG71IpVJiYmLm9SqiKOJwOLBarfT39+N0OlGpVPN1db1e/67atV6s\nia+MC6UL74Ij8eXS6dHAbrfT0tJCfHw8dXVnG4ycCxJfbSR+7wutjFo93FRQu0CBfjpCYog9g00o\n5TKuXySNfmpQyUpDQoKhEH9pbkSjkHNVYXHY97ga6JRKbinfwH/te4NgKETz2AhFiUlrTuSiKPJi\newt6pZLNmZEb3YiiyGvdLWgUcq4uXnmdPV39DMxYAajKiOdTtUXoVYu/N1EU+d2RdhRSCXdvXh3p\nLobXu2doHHPwuS1ZmNSrz6DEahV87/piHjjQz+9OTNM14+NfL0k4q05u9wZ5sH6WkiQtl+SGXwb5\nY8MYbn+Qr16Rs+p7O4XlxGSCIKDX69Hr9aSnz3niezweLBYLExMTdHV1Lai9G43GZeccLIdI9qNo\nx5C+33HRdvUChyiKYafOQqEQvb29TE9PLzkdDd7dSDwYDPLcoRYePz6XRk/RLR25NE4OMOm0cXNZ\nOTaPh57pKaacDqYcc18zLhcSQSDDFENOXBzZcfGkGY1nKcXf7O1hzGbjw5XVqOXnJjoGeLWzHVEU\nqUnO4/hEDw8d2sftG2pI0q/deMzjI0OM2mzcWFyJIgoBVPvUGEPWWW6rLJlXry+FwwPD7GruQAA+\nWVvIjrzUZZ/Jfb1jtE9Y+PttmcSGMRBlOdg8AX51eISCBC1XFUaeQZFLJXxxWza5cVp+/Zbo7YdX\nJJJpevt5+M1xC1ZPkO9eE76Kfsji4bm2KW7bkEJeQuRZkdVarqpUKpKTk0lOnkv5+/3++RT80NAQ\ngUBkrW2RuLXZ7fb5+7iIxRG62GJ2YeJUm1k4tWur1UpraytJSUnU1tYuuyG8W5G4xWKhsbmFXxwN\nolWoqEtbvGYsiiItU0McGelALpHwdFPj29cRBEwqDSaVjnXGZPzBIKN2M691dUJXJwqplKyYWLLj\n4siJi0ciCOzp7qI0OYWixHO30fRMT9E8PkpVci5VKXmkG+J5pe84vz58gJtKy1mfEr3xh8fvZ3dX\nB+nGGIoTI1/PHwyyp7eNNKOeTdlLR8reQICnT7ZzeGAYgL+/pIwN6QnLrm3z+Hi8oZvSZB1XFUZu\nxnMKDx8ZweEN8Plri6Lu+xYEgetKksiMUXPv7m7u3jXGty9NYHOGhr5ZH0+12bi6KJ7c+PCNSx4+\nPIxaLuXzO6JrI4zWN10ulxMXFzdv2LRUa9spUl+qtS0SEne5XBfT6cvhorDt/Ytw28yWI/FQKER3\ndzezs7OUlZWFldZ6pyPx0++xwR3PgGWIa3KrUCyiRB9zzHB4uIMJlxUBSDfEk6g1EqPWEavWYlRq\nFzUzcft9jNhnGLGZGbGb6ZqeAkAQQCpIuCwvOjX6cvAHgzzf1oRJpaUyaS6lmqg1cXPhFl7tP86T\njccZs1m5PL8wqo36je5OXD4ft5XVRiVsOjTYg9Xj4RO1i9vNwpyI7dGjJ5l0uAC4qih9RQIH+L9j\nnXgDQb64NSPqMa5NY3Ze6TRzc1kK62LXzhFsfYqB+24q5UevdfGNlyf4bLWJhjEPapmUO6vD1100\nDNs4MmTjHy/LJlYbXYYnGAyuaSviYq1tLpcLq9XK8PAwDocDuVw+X1c3GAzIZLKII/GL6fSlIQKh\n0MVI/ILESoYvFouF1tZWUlNTqa0Nf2N/JyNxm81GS0sLycnJxGWX8r+/PExuTDJZxoWpUbPLzpHR\nDgZt08iEuU3kipxyCuPD69NVyxXkxSaTFzsXbTt9Ht4caKN7dpyAGOK3Rw9wVWEJJUkpa67s3dPT\nxazbzQ15C+v7GrmS63NrOTjSzoH+XsbtVm4tr0ITQb1ywm7j6NAAFSmZJOmXt3tdDha3iyNDPWxI\nSyY3/uxSRkgU2dPVz3MtnajlckwqNRJJiJvLV673No2aOdQ/ycc2JJMZE52PuT8Y4hf7BknSK7m9\nau3tSxP1Sn54QzG/eLOPXx2bAeDTtakYw6y5B0IiDx0aJsOk4uMbw+8lXwqhUOicitMEQUCr1aLV\nahe0tlksFsxmM729vcBcmt7n8+H1elEuMzL3dFxUp6+M0EWzlwsTS5FtMBikq6sLm81GRUXFqns0\n34lI/PT6fFlZGWqNlo/9uh6pRMbW9LfFZTavi/qxbrpmRlFIZORoU+l3jZEXmxw2gS8Gd8BPr2WC\nbFMS5Qnr2D/SypONxzkeO8i1xeuJ065N5DBut3FooJfCuHRS9WeTolQiYVtGCQkaA/uGWvjVoX18\npLJmVeNTRVHk+dZmVDIZO3Kia1t7rbsFiSBwU9nZmQmr28MfjzXROWmmID6JRJ2Bff1dfHFHGSr5\n8h9PbyDII0c6SDcq51uzRFHE4Q0y7vAxYfcyYfehlEnYkKYn1aBc9jD1p5MTDFu9/OvVBShl54bc\nlDIpX9i2joZhK05fkFc6zWzKMoVlSvNs6xRDFg8/v6006vY5eHfGkCoUChITE0lMnDtQB4NBRkdH\nmZiYoK2tLezWtovq9OUhIlyMxN+viGQIyuzsLG1tbaSlpVFYWBhRVCmVSvH7/at+3XI4/T5OqeMT\nEhLm6/O/PTjIiWErl2aVoZYrcfu9NIz30Do9hIBAvi6DXF0ah2aaUMvkXJJVGvG9BEMhXuttRCmV\nsy29FLVcwQcLttA6PUj9WCcPHNjLluxctmXnRTUFLSSKPNvSiFIqoy61YNmfLYxLJ0al49X+4zx8\neD/XlqynMvXs6V+L4eToMIOWWa4tLI9KmNc9PUG3eZIb1xdi0iwkquaxSR4/1oQ3EOTqgjKyY+J5\nuH4vFWlxVKUv32suiiK/OdTGlNPDtmwTP97dx7jdx4Tdh8u/+GExSaeYn0xWkapfMBRl2OLhiRPj\nbM+JpSrdFPH7DQdPnhzH6Qvy0ao8nmkZ4Et/6eArO7PYlLX0da1uP39sGGNLtomdywxGWQ3Oh1ni\nUqkUjUZDTEwMubm5Ybe2RRuJDw0NceeddzIxMYEgCNx9993cc889a/jO3mW8R2rigiBIgXpgRBTF\nGyJZ44Ij8ZVwenQbCATo6urC4XBQWVkZ1dQgqVSKx+NZq9uchyiK9Pb2MjExsaA3vd/s4qevdpNl\nTCA/NpVB6xSvDzTiDfjJ0qRQaMhCLVXSauvD4nNyfX5VVGR1bKyHKZeNK7Mr59eRCALrE7LIMSVz\naKSdN3u7aR4b4eqiUgoSzrbwDAf1Q/2M2qxcllWOSrby/SZqTXywYAu7+0+wq7mR48NzWYEUw9Lp\ncbffz6ud7aQZTJQlp0d0nzBXt3+tu4UkvZYdeW+LsBxeHy+0dnGgb4gknYHbKzYQp9XxVHM9IPLx\nmoIlDxohUeTE8DRPnuhh1DZXOz8yaCNBpyJepyY3IZYEneq0LzV2r5+m0RmaR2d4o2eWF9qnkQhQ\nmKClKt3AhjQ9vz06ikIm4dN1mRG/33AwYnXzdNMYW7KTubokk5qsRH6xt4l/f6WX2yuT+VhVyqJi\nut/Vj+IJhPjGVXlrVpo5H0gcFgrbzmxtE0URj8eD1WplYmKCJ554gt/97nfIZDIOHDiA0WiMaBKi\nTCbjJz/5CVVVVdjtdqqrq7nyyispKYlu8t/5hPeIOv0eoA2IuJ3mIomfgVORuNlspqOjg4yMDIqK\nljZGCRfnypfd5XIRDAYX9KaHQiLffLoVAQlbM4o5MtrJiYk+THItWxMr0MvnSgEzPhtd9kGK4tPI\njomMVAGmnDbqR3vIi0kh23S2Gl0jV3LZugqK4tLZP9zKY8frKUxI4rri9ehXYW9pdbvZ3dVBhiGO\n3JjwxVAauZLr82rpmBnh6Ggnvzq4j6r0TC7LL1y0Vr67q31NxGyHh3qweNx8vmYjMokEjz/Anu5+\nXu/qwxcIUpOezSU5hcgkUrqmJ+ianuBDlbnE686ubYdCIvVDkzzb3M+QxYlUIqCRS/nXa6tIMWiW\nvU+NQkZSYRpXFKYRCIXonrLRPDpD09gsf2wY4w8NYwBclh8fUU94uBBFkV8dHEAulfDhqrkRrnFa\nFd+8qopHj3Ty2IkxOqdcfP3SdfM+6ADd0y5e7jBzR20aOatQsa+ESARl5wIr9aur1WrUajXJyckU\nFhZyyy23cOutt9LU1MT//u//YrfbeeKJJ8jNDX8sbkpKCilvGTnp9XqKi4sZGRl535C4CAQjG/D4\njkEQhHTgeuD7wJcjXeeCI/FwNuWhoSFkMhkbNmxArY5OLHQKa+3LPjAwwOjoKCqVivz8/AXff/TI\nEA1DFjanFbG7v5Fxh4V1mhTKTLlI3xKwBcUgJyzt6JQqtmdGbsYSDIV4ra8RtUzOlvTl10nVx3FL\n4VaapvppGO/mV4f3cVtFNRlheJ2LosizrY2IImxLL101uQqCQFFcOtnGJI6Nd9MwMkjrxBg78wqo\nSc+cPwCNWi0cGxqkKm1d1GK2w4M9bEhPZl2ciTe6+nmtoweHz09BfBLbsgtJ0M6lQ33BAK91N5Nm\n1HJ18cL2s2AoxOH+CZ5tGWDM5iJRp6UsNZmm0XHu2lFMqnF12gyZREJRkomiJBMf2gDDFgffeaEB\nAYHdXdNMOrz83ZZ1pJnW5rk/HQf7ZzkxYuOOmnxM6rcFXAqplE9vLiYn3sCjRzu55y/t/L8rcsiN\n1yCKIg8eHMKkkfN329d2Ml0oFHrXB5/A6g8T8fHxhEIhfvSjHyEIAl6vN6rDSH9/P8ePH6euri7i\nNc5HvAcc234GfB2IStzw7j/B5xGmp6cZGBjAZDJRUVGxporqtSJxl8tFc3MzRqORuro6Dh8+vOD7\nA2YX973STYLGwPHxbgJiiOqYIjI0CyPtVmsfNr+bDxRG52l+dLSbaZedq3OqwkpvSyUSKpNyyDQk\n8HJfA78/epBri9dTlb58GrdpbIQe8zRb0ovRKyOPxpRvHTaK4zI4MNLKC20tNAwNck1xKZkxsTzf\n1oxWoWB79vL19pXwanczUolAutHAD15+E4vbw7qYOG5ZX0SKYWHtd19fJ1aPh89vr5p3wgsEQ+zv\nG+e5ln6mHB5SDDruqKkkSa/j53v2U5uVQHXG8nXzcPD0yQFCIfjX62ronLTw5Ike7nm6mVsrUri1\nPHVNBGQAHn+QXx8eJDNGx2UFi4snd+ankRmj5xd7m/jqMx18cVsmUolA64STb1+Xj0G1ttvV+ZRO\nX81MhTMd3sJVtC8Gh8PBrbfeys9+9rMFNtHvdYgiBN9dYVu8IAj1p/37IVEUHzr1D0EQbgAmRVE8\nJgjCzmgudJHEmXNeam9vx+/3k5eXh8fjWfOWqGhJXBRFhoaGGB4ePmsm+SmHuVBI5Jt/aSUQFJly\n2TDKtWyNKUEvX0h6U95ZepwjlCVmkmGMnAgmHBaOjfVSEJt2VvvaSohV6/lgwWZ295/k2dYmxu02\nri4sWbQf3eH18lJHK8laE6Xxa1OzjVHruC53I33WCQ6PtPO7o4dIMRgYs9m4rqgiqoNN19Q4PeYp\ndAo5z7R0kmowcU1BxaKDUcZsFuqH+7gkL5WCxDlyPzkyze+PdDDj8pJuMvDJ2hKKk+d+vw/sO4RK\nLuUTG/PPWmu1ODY0zdHBKW6pyCXVqCPVqGNDegJPNHTz+PFR9vaY+dyWdVSmRZ6ROIUnToxidvr4\n221li/6NTyEn3sC/XbeRX77ZzE/3DKCWSyhK0nLzGkxkOxPnE4lHEklHu0f5/X5uvfVW7rjjDm65\n5Zao1jof8S5H4tOiKNYs8/2twE2CIFwHqACDIAiPiqL48dVe6IIj8TMf/MnJSbq6usjOziYlJYWZ\nmRkcDseaXzcaEne73bS0tKDVaqmrq1vwgT/VKy6VSnnwzX6ODVoAyNIkU2bMO8sj3RcKcNzSQYxK\nw5aMyFun/MEgr/Y1opUr2JwWmamLSqbgmtwajox2Uj/Ux6Tdxm0V1WjPiCxeaG/GFwiwI2/9mh6u\nBEEgx5RMpiGBo6OdNE0NAPBqZzNtEyOkGWNJN8aQYjAtapIDcwcop8/LlNPOlNPOhN1K+9TY/Pu7\nqqCCvLjERe87FArxUmcjRrWCD2/IxRsI8kRDN7u7RkjW6/jMpjIKEuPnX7u/d4D+GQuf21qEUR2d\n0YnLF+D3hzvJMOm4uuTtg5FRreSuraVszUnh0aPt/NuLHWzPieXTdZnEaCK75pDFzV+bxtmem0J+\nwsoHAoNKwVcvr+T7LzXQa7bxzavzonaOWwxrbfYSzX2shsTXYvaDKIp85jOfobi4mC9/OeJy7HmL\nuZr4+StsE0Xxm8A3Ad6KxL8aCYHDBUjip+Dz+WhvbycUClFTUzOfklrJ7CVSRELioigyMjLCwMAA\nRUVFi6pQT607avXy89d7EIBKUwFZ2sWFX42WLtxBH9cVbFp0jni4ODjcwazbyfV50aXjJYLAprRC\n4tV69g4186tDb/LhDRtJfUs93j4xTtvEOBtT8jGpzo1DlUwixR3wIxEEKuJzcfrdTLkt9M12zt9j\nok5PmiGWNGMM/mCQKaedSYeNaacdl9932loSQqLIpoxctucULuugdnS4jwmHnS9sX8+E3c1DB1oZ\nt7nYnruOa4oLFrTizbrcvNjWQXlqDFuyIxchnsLjDT1YPD6+cEnFosNsSlJi+c71dTzfMsDzLf00\nDFv5RE0GVxUlrMoVThRFHjrQj1Iu5bYN4QuvphweBmft3FiWSFVG9JmAxXCuzV7CxWpJfDWmMEth\n//79PPLII5SVlVFZWQnAD37wA6677rqo1j1vIL7rkfg7hguSxCcmJuju7iY3N/esIQLnQkUeyboe\nj4eWlhZUKhV1dXVLCnAkEgn+QJCvP9WCVJCyMbaURNXiQrER9xTD7kk2puaRrIu8F3jIOk3jxADr\nE7JI00fv1Q2QF5uKSaXjlb4GfnvkADeUlJGfkMTzbU3EqXVUJGWvyXUWw7Btmu7ZUcrjsymLf/s6\nvqCfKbeVSZeFKbeFk2ODHBvpB+bI2qTUkaqJJ0alJ0apQ0DglaFjrE9K45Lc5bMTFreL/QOdVKbF\nMWJx8MC+FnQqBXdt2Uh+wsK0uyiKPHmyCQH4VF1kPgWno33CwutdY1xVlEl23NJ1ULlUygfKc6hb\nl8SjRzp44EA/x4Ys/OPOXDSK8EjnjW4zTWN27qwtxLDEBLYzIYoijx7tQCmT8OXLIp9SthLeq+n0\ntZhgtm3btnMyzfF8wXtBnX4Koii+AbwR6esvOBIPBoOYzWY2bty46OjAcxWJhzs2VBRFxsbG6Ovr\no6CggISE5b2zpVIpjxwZpmHISpWpcEkC9wS9NFo7SdIaqEkNPyI6E96An9f6GjGptNSuYLayWsRr\nDHywYAuv9R/nL80nSdDqcPr8XFVYjUQ4N5ttIBRk/3ArBoWasriFBwWFVE6aLp403RyphsQQsx4H\ncqkUnVyzICIVRZGXB+tRymRcmru8Sl8URV7qbEQiCMy6vJwYMVORlszN5esXnW52bGiEzkkzn9iY\nR7wu/Ja8xeALBnn4UAcJOhUfrAiPIJMNWr5y+QZ2dw7z2LEuvv5MC9+8Ip804/IKdrs3wG+PDJIb\nb2Bnfvg2rseGpmgem+UbV+YSrzt3E/DeqyRut9svurWFgfcKiUeLd/8Jfochk8koKSlZcvbvuYrE\nw4mefD4fJ06cYHp6mtra2hUJHGDEEeIXewZJUcWdpUA/BVEUOT7bQVAMcUVOxbywyB8MMOW00mke\n5eR4PxMOC6EVTud7B1px+n3szCxfciZ5NFDLFVyXt5EsYwJTTgdauRKdYu3bnU7hxEQvVq+L2uRi\npCu8H4kgIU5twKDQnpVS7rGOMuGycElOERrF8qnOlokR+mfNBEMhJh0ePlpdwR01GxYlcKvbwzPN\nbRQmGrm8MHq/8L82DjBuc3NnbfGqrFUFQeDywgy+cvkGrO4gX9/VyrEhwm3r0wAAIABJREFUy7Kv\n+f3RIezeAJ+qKwo7Be8NBPm/+i7WxSi4sdh4TqPF92pN3OFwrNr2+YLDW+n0d+vrncQFF4nD3Ia0\n1OYglUrPSSS+EsbHx+np6SE/P3/eV3kl+IMhfnHUjkSQUmFa2uWryzHMhHeWvJhkmiYHmXU7sHid\n2L1nO8gppTJS9bGkG+LIMMYRo9LNr9s9M06HeW70Z6L23NQpYS46NrvtqKQKXH4PT3cc4MrsKuI1\na9sCM+txcGKilxxDCqnayMsCnoCPhqku0o0xlCcvPWYUwOx08GLH3JjXzBgTH6mqIEaz+CFFFEWe\nOtlMMBTiM5uXr6+Hg36znedaBtmak0JJSmTWpUVJMfzLNRv5772NfO/lTj5ek84t5WcPuGmbsPNK\nxxTXFGeSERN+6veZ5n7MLi/f2J7C0MCc7ahGo5m3HV1qnGckeK/WxC/6pq8METgHsdh5iQuSxJfD\nO30y9/l8tLW1IYrikin+pfDg3n56LX42xpagkp79Ok/QR7O1h2H3JADds+PIJFIMcg2xciNZmhQM\nci16hQaFRMaUx8Kke5ZJxyx9lrnXaOQK0g1xJGgMHBvrIUFjoCo58nR8ODg00oHT52F7wgYE4Ohs\nK7u6DrEjYz15sWszXUsURfYNtSCXSKlOiq4scGyyC18wwFUFZctmXPpmpniquZ6gKLIjdx3XlS4f\noR4fHqVtYoqPVeeSbIjOqSwQDPGrg+0YVAo+UhVde1q8Ts0/XVXDbw618kj9MH1mF1/cno1KPkdE\ngVCIX+7vJ06r5OaK8LUM4zYXL7YOcsP6RK6tmbtHURRxu91YLJb5cZ4KhWLBOM9Iifh8SaefahEN\nFxfT6eHhfVzyX4CLJP4uYmpqis7OzkUFdiuhedTG/+zpI12dSJp6YdrdFwrQbR+ixzFEEBGJIFAb\nX0yC2oRauvQkqyxdMlm6uftw+N1MumeZcM8yaJmm0zzXNpVjMhESRc5Bxw8wJzJrNw+Tr8sgVjEX\nee+Ir6J+tpXdA41MuWzUpRVEXSPvnBlhzDHL5pQS1GGY1CyFcecMPdZRNmXmzjuwnYlAKMje3g6O\nDvcBUJeVwQ3rl6+b2z1edjW3kpdg4KqiyP3bT+HZlkGGZp18cUc5WmX01qpKmZTPbV1PZswAT53o\nYdjq4ZtX5JOkV7KreYLBWTf3XFIWdsp+TszWiVIm4R92ZODz+ZBKpQiCgEajQaPRzI/z9Hq9WCwW\nJicn6e7uRiKRzE/9MplMYbuwnS8kDqvr+b44hnRlzJm9XBgsfkGS+HLp9HN93VAoRDAYpL29nUAg\nsKC9LVx4/UG+9mQLComcclPe/P8HQkH6nCN0OYbwhQJoUOLCS11CCZm61bUl6eRqdHI1OYZUemwj\n1E93YJTraJ0eZMQ+zdb0EtIN0TuGnQ5f0M/eoWYMcg1FhnXz/6+SKtgSV06ztZemqX5m3DYuz64M\nyyFuMbj9Xg6PdpCkMZFnjDyyD4ohjky0Y1Kp2ZK1eHQ77bTzbNtxJhx25BIpsVo1Hyhf3p/6VBrd\nHwxy1+YiJFGemIZnHfy1aYDarEQ2ZKyss/j/7L15dGRnee772zWq5kEllcaW1GrNrZ7Ug+32RIwZ\nDJgAAUwSiK8JcUI4h+RCiA+HnECSe0OSmwMJsBI4BEJIgnGwsc1gg23cxhNtt9vq1jyrpJJKQ0k1\nz7X3d/+QVT1oKlWp7ba7n7W0Vqsl7b1r2s/3Pt/zPm++kCSJ2zrqqbWb+cazffzJw3387jW7uPf0\nDIdqXds61+lpP72+Zf701kYqHSZkWUYIkfu8wIpKJkkSer0et9uN273yns5kMoRCIYLBIB6PByEE\nVqsVu92O3W7fUN0SQlw2JL4dxGKxot3pVwKuVuJXOLYrceUDtVrN4uIio6OjuXCZQs7x5V+MM+6P\ncW1pJzqVFkUoeOJzDEc8JOQ0DslKnWRnVExRZ3Zvm8DPRzQTp3t5hHK9netc+1hMBTkbGuGnY6do\nsLu5rroNk644x/QqzpfR1RdV2ipJxT77HmxaM2dDw0Xtkz/nHSAjZzlW0VbUa9znnySYivEbnUfW\njFcVQtA9O8UvxvrRqtRUmUvxRZf4wMHOdfuyz8eZGR99cwt88NBuKm3nZPSsorAcS+GPJgmnMjSW\nWiizbG76kxWFbz4/hFGr4TcPFzcXfSN0Vrv4n287wldOdPO/T4yjUUn8Zlf+kn0yk+U/Tg3TVG7i\nt47VoFapchK5oig5Ml/9WiV1SZJQqVRotVpcLhcu18qiUpZlwuEwwWCQmZkZMpkMFoslR+olJSU7\n/tl+NRGJRAqaXHYlQYire+JXNM5PQdspZLNZ4vE4Ho+Hrq4uSrYxvet8nJxY5tvPeag3VeIucbKQ\nXOZsaIRoNolNMrFHVYcZA2fEEEatnkOuwm/cihCcXOxHhcRBx0p/cnmJgzfpDzMSmWY4NIU37Ker\nsom9ZbuKkrinw4trZPT1UGeqwKo1FrxPPhVaYCw4xwFXI3Z94dVMMBWlZ2mc1rJKGksvNCLG0yke\nGTrL6NIC1eZSmhzVnJg+y417Gqh1bN6fvxyL88CZXsrMJcRTGf75mQH80ST+WJJAIrWmuqiwGuis\ndLKv2kmr275Gvn50wMv4UoS7j+/FkmefdiGosBq5bW8933p+gKwiuL97nDuvac1LTn/w7ATL8RRf\n/WDHmgXOaqW8HqkLIZBleQ2pS5KEw+HIRRMrikIkEiEUCjEyMkIikcBkMpFOp3NO79eK1AtRBKPR\nKHV1OzsM5o2IK6XF7Iok8a0+sKu94jtF4svLywwMDKDT6Whvby+YwCPJLJ95oB+z1kC7ZTf9oQmG\no1MYJT3tqt04sCJJEqPKFHGR4k2ug+hUhb/Eg0EP/mSYw85WjJpz16yWVLRa66g1lnM2OMqvZgYZ\nWfZyvKaDCvPWE8kuRlrO8PTUWhl9Izh01gv2ySdD81xT3bplK1pazvKMtw+H3kSHa+vzbAQhBL/y\n9aNVq3lzU8cFP5tYXuSng2dIZNIcrWihyVHNj8afx2Uy8paWjavTRCbDc+MeHh8aRRaCZFTmx/3T\nOAwlOIwGGl2lOI0GHEYDTpMBg1bLuH+ZwXk/T436eGxoBq1KRXO5jX3VTjqrnKgleODMJAdrXByp\n2162/XYRS2X4wctj1NittFeU89jgKN5glP920z7KN1ELpgIRfj7o5f2HqjiQRzLbeqQO5OT3VUKX\nZRlJknJfNpsNm83Grl27VqJyYzHOnDmDx+MhGo1SUlKSq9QtFsurJrMXkpt+1Z2eH8TVPfErFzvV\nKy7LMsPDw0SjUQ4dOsTo6GhegS8b4S9/Osh8OMlRZwcvBHrwp8K4pVJ2SzU5+XlJhJgTS7TadlFu\n2D6hriKQitAbmKDaUEaNYX0CMGkMXFO6F19yiZ7QKA+PnKTdVcu11W2bDrm4GM97B4llUuvK6Bth\ndZ98ODLFSGiaqfAiB9yN7Cuv37B//YXZYaLpFG+v35/3edbDSHCGhUSIt7fsw/RKT3gwEeeZyWH6\n5mdw6E3csvsQToOFF3xDhFMJ7j58FN06VWk0leLpsUmen5gi+Upr45FdVbytbQ82Q8mmz2ON3cqN\ne+rJyDLj/gCDC36G5v1876UxvvfSGBrVCoF9qGvj9sOdwn+9PEo0leGua45QbbdS67DzvVPdfP6R\nF/n94x3sq14r/ypC8G8nh7AZNPzxLYUls62S7fmkuyq5r1bswJp9dbPZjE6no6OjAyEEyWSSYDDI\n7OwskUgErVabM8rZbLZL1opWCIlfNbZtjRVj22t9Fa8OrpL4OtiJ1LZgMEh/fz81NTW0trYiSVJR\ni4NH+uZ56MwcNYZyuoNDZIVCs1RHuepcv29aZBgXUzj0ZvY6C4+rlBWZk4t9lKi1HHA0bUoAkiRR\nZXBRrncwEJ6k3z/NUiLMrQ0HMWq3Vhw8oQWGlmdo3kJGXw8qSUWrtZ5dxgp6w2Oc8o0wsuzlmuq2\nNVPV5qIB+v1TtDl2UWYovMc9nklyenGEOnspnRU1RFJJnpsc4ezcNCpJYq+rnoPljWhUahbiQfqW\nPFxTX0uj60ISCyWSPDU6wUnPFFlZocFZxmw4QLnFyAcP7d3WIkirVtPidtHidkHnSs76j3qHednr\nAwRfOtHNh4+00uIufFG3GQbnAzw9NsvNTQ1U21dew1Z3Gf/95uP82wun+dKTZ3jP/gbeubf+gpa6\nX47OMuoP87F9eobOns6RpsPhKCobXKVSrSH1879gxQy3SvaSJGEwGDAYDFRWrswcSKfTBINB/H4/\n4+PjF1Tzdrt9W6NDN0OhJH7V2LY1lKuV+BsXW1UlxZCtoiiMjIwQCoXYv3//BclKhR53Ppzifz08\nQIlKhzexgFkqoUNqwCidI0khBGNimiwKR8vai6o0zwbGCaXjXOdaMc7lA41KTae9EafOyungID8c\nep5bGw5Sbtp4DziZTfP0dC82rYmWPGT0jWDUlHDU2cFCMkBveJSfjZ+m1uriuuo2bCUmsorM09O9\nmLUlHCgvrsf9hflBFKFwY0MLT44N8PKsB0UImh017C9ryC1csorMc7N92A16bms/50tYisU5MTLO\nqWkvQkBbeRXHaht5ZnKYrCJzR9fmozrzgawI+nzztJSXcU39Ln7U28/fPn6a6xsref/BJsw70GK2\niows892Tg5SaDNx60XZBqcnIH95wLfd39/LAmQnG/WF+73gHRp2GcDLNf708xuE6O3/07gMoipJz\nmJ9vRlvd2y7GjHYxqcfjcXp7e6mpqdnQAa/T6SgvL88FL2Wz2dz1TU9PI8syVqs1R+qFbpEVKqe/\nkWZ/XwoIAUWInq8rXJEkvhUKrcRDoRD9/f1UVlZy5MiRNTedQieZfeoHPUSSWQRQIZXScJ58vooF\nscySCHHAuQe7rvBV+kIiwHBomgZTFe6S7ad6VRvLMGsNnFzq40cjJ7m+toOW0vX7nJ+d7ieZzXDU\n1VnUomMV5SUObtZ3MR6dYSjq4QeDz9BZ3oAQgkAyxi21B9EW4RHwhOeZiiyyy17K98+eJCPLNNqr\nOFC+G4vuwjCW7oVxAskYH73mMCVaLclMlp/0D/Kix4sE7K2o5WhtI3aDkaFFH8P+Od7R0USltTiZ\nVBGC75/uQSWpeO/+vdgMBhpdLp4YHuHpsQnOeP28/1AT1zVU7IjE/qOeSeYicT523ZF1twt0GjV3\ndO2j1mHjx72DfOGRF/lvN3XySP8UqazMn9/WnFOpnE4nTufKe27VjBYIBBgcHCSZTGI2m3E4HNjt\n9oLNaMvLywwNDdHW1obdbs+daysHvEajobS0NOcKl2WZSCRCMBhkcHCQdDqN2WzO7asbDIa8rq8Q\nA+1VOT0fiC0jpN8ouCJJfKcrcUVRGBsbY2lpic7Ozg2lrkJI/G9+NsKLniAqJJqkXRfI56tIijQT\neCkvsdNs2zz2czNklCwvLPZj0RrYaytcjrdpzdxcfogXl/p5aqoXfyLMtdWtF7jXxwI+xoJztFnr\ni1p0XAyVpGKPpZYao5u+0Djd8+MAWLQGktk0kXQcsza/G+wqFCFYToZ5zteHBEwFl6i3ujlY3rju\neNTFeIhe/wRHdtXQ4i5jcinAvafPEIgnOFhdz7HaRsz6lcotlk7x+EgPtXYrb2oqflLb8xPTjPoD\nvHd/JzbDiqFMp1Hz9vZWDtZU8cOzvXzr+X6eHZvlI8daqbAWnsHtDUZ5pN9DV201zeUbZwZIksT1\njfVU2638+4vdfOGnp8goCndfX0dj2frnV6lUOfm6vr4eIQTRaJRAIMD4+HgujnVVfrdYLJu+pkII\nPB4Pfr+fQ4cOXSDX5+OAz2azOZPcarW+StirfxOLxQgGg4yNjRGPx3PXtxoXu971FWKgvZrYtjUE\noMhXSfyKxXYq8UgkQm9vL+Xl5Rw9enRTV+t2SXxsMca/vzCNFjV7pSZMqrUuXyEEI8KDJEkcLSuu\n7/nlpRHi2RQ3lB0oeriJTqXlWtc++kLj9C1OsZyI8Ob6gxi0OuKZFM9O9+PQWWgy7yrqPBuhRK3j\noKOFQCZMPJskmU3zrK8PAKNGR5nBQbnRTrnBjqPEjEpSIYQgnk0RTEUJpKIEU1FCqZWceVmsaHPl\nRhvXVLZRalhfzpQVhWdne7Ea9LytvZlH+oc4MTKOzWDkjgPXUmO7cBH2xGgvaTnLhw4XL6MvxxP8\nqHeIprJSjuxaq35UWK3cffxaXvRM8+jAIH/+k5O8vaOed3TUrelz3wqKIvjOrwYwaDW8a+/mY1dX\n0VDq5OPXH+NLJ56lwqzn7hvyb5OSJAmLxYLFYsk5zOPxOMFgkKmpKSKRCHq9Pie/W63W3GdRlmX6\n+vrQ6XQcOnRoS+d5oQ741eurra294Pqmp6dzcbGrpL56fYXI6el0uuh54m94CJCvkviVi3yGoCiK\nwsTEBAsLC+zduzevlbFarSaTyeR1Demswqd+0IukqDigakMnrb+POSsWCYkoR0pbMWkLn/Y1G/cz\nEfHRbKmlVL8zw01UkkSnvRGb1kx3cJgHh5/jzfUHeWluhIyS5Xhp/tOtCsFodJpoNsEBUzNubSlR\nJUEgGyaQDbMYD+KJzAOgVamx6oxE0gnSyrnX3aDWYZKMuDR25jPL7LFXcUPN3k3P2b04RiAZ4z37\n2vmX519kNhRhX0Utb2psR3dRHOjQoo+hxZ2R0YUQfP90LwDv3b9vw8WcSpI4Vr+L9go3P+kb4Ec9\nE5yamucTN+7fVj77L4a9jC+FuaNrHyZ9/v3np6ZnSWVl/vJde3NZ64VAkiRMJhMmk4nq6pXpbqsZ\n67OzswwODqLRaDCbzSwtLVFXV0dNTWHxtYU64C++vlUH/Pz8PCMjI6jVatRqNXq9nmw2m3dc7MXX\nchVrIYArxNd2ZZJ4Pn3iqVRqw59Ho1H6+vpwOp0cO3Ys7w+UWq0mmVw7OWw9fO3EOANzEVpVDRsS\neFwk8IhZqo0uGiyVeR13PaTkDKf8g9h1prz6tLeLXSY3Fq2RF5b7eGjkVyhCsNfWiEVb3FCPzRDO\nxBiMTFKhLaVCtyL1WtRGLGoju/Qr+fAJJUUgGyaYjRDLJnBrS7GojJjVK186lZaskHk+0o1Nb+Ta\nqs3zzv2JEL3+SWrtNn7UO4hOreE9HYfZ41qbmBdPp3hitHfHZPSTk16GF5b49c6ODaeinQ9LiZ47\nug5wqLaa75/u5q8efZG7j3fQWb11lK4/muD+7lFa3S4O1eQftDMfjvDkyBjv6nRzvLGwKWqb4WKH\nuc/nY3R0FLvdzuzsLLOzszn5vViHeT4O+FWSX82ALykpoaKiIjcnIZPJMDY2RjKZpLu7G+ACB/x6\ncbGvRVz06xLiqpx+RWOjSnx1X212dpaOjg5stu1VrPnK6ac8Qb7+zCRuyYlLWt/drbwio+vUGg65\nWohnk4QzcSKrX+k4CTmJVWfGbXDiNjgwa9bfC37JP0hKznCtc2cMZuvBobNw1NHBU4unAUhkk68M\nUtn5SlwIQXdwCI2kps24MUEaVHoMujKqdBtnfI8kpojJKd6+68imWwyyovC0twdJgulgiMbSct7a\nfK6P/GL8YqyPZCbDh7qOFC2jB+NJHuoZZHepk6P129ueaC4v4xM3Xs93XzzFP5w4w3sPNPL29roN\nF7pCCP7t5CCSJPHe/Xvz3r5RhOD+M32YdGr+9C17tv6DIiCEYGJigkAgwLFjx3JkuJqxHggEmJyc\nRFEUbDZbjtR3uq1tVXrfyAGv1WoxGo04HA7cbjfZbDYXF+v1eslmsxs64Is1JT766KN88pOfRJZl\nfvd3f5d77rmnqONdjrjaYnYFQ6PRrCHb1bYUm83GNddcU5CclQ+JR5NZPn1/LyXoaJDWl/9koTCg\njBMhgVHS85Op51A494bVSCoMQo8WHf5sEG9sEQCTRk/5K4TuLnFSotExFZ1nOrZIu7Ue2w4azC6G\nEIK+8BhqSYVd2BiLzRDJxjjsaEen3rmWJ4DRqJfldIR9pib0qsKjRgPZMJ6UjzZnLRWmzXusT0yf\nIZiKo1GpeGvzXjorajee7+6fY2DBx9vb9lBpK15G/6+X+1AEvO/AvoIWRQ6jgd8/fh0/6D7L/d1j\nTAci3HlN+7qRqc9NzNE3t8x79rXnVfGv4gXPNBNLAf6f21txmi5d/Gs2m6W3txej0cjBgwcv+Jyu\nl7G+Super5dMJpMbnOJwODAYCt+e2swsd74DPpVKodfrURQFjUazrkM/GAwyPDzMt7/97Vx7W39/\nP21thXlgZFnmD//wD3nssceoqanhyJEj3H777bS3bz6Y5/UEIcTVSvyNjHxjV2HlzTA9PY3X66W9\nvT3nRi0E+ZD4Xz0yxFwoSaeqGY104U1UEYIFsYRH+MiQRY0KfVaPHSsG9JSgx4AerdAgIeWuP0ma\nEBGC2Sje6AITkZWxolatgVg2hV1npslyaQxmqxiPzrCYCtFILRVSKXZhZjzl5Sn/Sxx17sWm3ZkF\nRDQTZzAySbnWSaW28ClrslDoS4xh0ZXQ5d44LjUlZ3hq+iwz0SUMWi2/dfA4DsPGju9kJsNjIz1U\n2yzc0lJ4B8AqTk/76J9f5J0dbZSaCt+e0GnUfKjrAFU2Kz8bGMIXjvOJG/fhMp8jslAixfdfGqah\n1ME1Dfm/X8LJJD/tG+JovZ1f37+9kbvbQTQapbe3l/r6+rxG+67X1rZaCV/c1uZwODAajUX1qq+e\nc/VcMzMzhEIhamtr13XAwzl5va6ujr//+7/nxIkTfO5zn+MLX/gCAwMDdHV18e1vf3tb1/LCCy+w\nZ88edu9eef/dcccdPPTQQ28oEgeutphdyVgl20QiQW9vL2azmWPHjhUdvbgViT/aN88Pu33UShVY\npXNEIIRgUQSYxkdCpFEpEhqVioO0od3iJZSQMLxC7hW4VnKjSRAkgi+ziIxCLJPAE/NRbypsqtpW\niGTi9IUncGLFzcoN0y2VYhQlDMuT/HLxZQ7aW6gxFpfvLYTg5eAQKiTajbuLeiyjyRVT3Fvqu9Cq\n13+O52IBfjl9llg2hU6t5q7DN2HcQD5fxZNj/SQyGe4+3lW0jB5Jpvjh2QF2Oexct7u+qGPByuL2\n5qZGKqwWvn+6m7989AU+fsO+XNLbf7w4RCqr8BsH9m6r4n/o7ACyovD5d7RcsvjXhYUFxsfH6ejo\nKLj9anUuud1uX9PWNjo6mmsbW5Xft2pr2wirgVCpVIrDhw+jVqvzdsDv2bOHhoYGvv/97yOEYH5+\nftvnn5mZobb2XCtqTU0NJ0+e3PZxLmesTDG7MtJerlgS32ymuFqtJhqNcvr0adra2nIr9WKxGYnP\nh1P82cMDWCQjtdJKFSGEYJkw02KWqEhSktFgSeqJWFLsoXZLAl8PEhJmjKTIkEHGLTtJqJJ0B0fw\nxHwccLTsaN+2IgQvBQZRIdHIhRKzRTLRKZoZYpJTgQGCmQjt1t0F75OPx2ZYSofpNO6hpAgZPZSN\nMpmcoclRTbV5vcxvhZcXxuhZnMipJe9sO7glgU8sL9A77+XWlt3UOorvAHjgzACpbJb3HejcUW9B\nq7ucj99wHd994SX+/omXuaOrCatBx0vTi7y9vZlyS/7vj/65Bc7OzvHf39RAfenOGxmFEIyNjRGJ\nROjq6tqxOFTYuK0tEAjk2tpWB6dc3Na2ETKZDD09PTgcDpqbz2Xa5+uAn5iYIBKJ5K4vH8XhSsUV\nUohfuSS+EZLJJL29vWQyGW688cZttX1shY1IXAjBZx/sI5ZSOCDVoZIkgiLClJglLOLosmrKAxb0\nKQ2z1UEcWCilcFk/i8yk5MUkSqhVKpAUWJJCeJnjxMJL7DZX02atLyrdbBXDkSkC6Qgt1K/rstdJ\nWjpEIxPMMhr1Es5EC9onj2bj9IcnKNM6NjWqbQVFKPQlRjFq9RypaF7z81AqxtPeHhYTYcp1ThbT\ny+x119BYuvnM9lQ2w89HeqiwmHhL64XGLkUIoqk0wXgSq0GP3bB1hGfP7DzdM3Pc2tqM+xIEf5SZ\nzXz8huu493Q3/3FqGK1aRZXNwk178nfSJzNZHjzTR2OZibuu2/ntmlVCtFqtHDhw4JIPeTm/bWy1\nXW29trbVSt1ut1+g3q3K/bt3787FuW6Gi81yZ86c4U//9E+56667inoc1dXVTE9P5773er25Nrg3\nClbUjKuV+BUFIQQ+n4+JiQmam5sZGRnZUQKHjUn8ey/O8MzYMo1SDTp0jChTzIsltIqKsmUzlujK\nTX3OHQJJYjc1uT3vQjCFj5TI0pitRfXKcVzCjj1jYVo1z1h0htnEIp22PVQZXAXfHIPpCINhD2XY\nN3TZw0rKWiM1mIXhlX3y0xxxtGPX5UdOQgheDgyhliQ6jI1F3czHkl7C2ThvrjuI/ryFhBCCkcAM\nJ+cGUaHioKWZsaQXs17Pm/ZsvZf4+EgfkWSSY3W7eXxojEAiSSCeIBhPEkgkyZ4X9FxpNdNWUUab\n20V9qWPNjO1EOsP93f1UWi3cvKf4ffWNUKLV8pGjh/nHp55hLhxBlhUiqRT2PA1fj/QPEUwk+dod\nh9Cpd7brIRKJ0NfXlzchXiqsNzglEAjg9/sZHR3NzTaXJInFxcVNEx03ghCChx9+mL/927/l/vvv\np61t81bHrXDkyBFGRkaYmJigurqae++9l//8z/8s6piXI5TsVRJ/Q+N8OT2VStHf349Go+Ho0aNo\ntVpGRkZ2/JwqlWrNKNLJpThf/NkwDsmCFRNnxRAxkcQeNOAImVCJFUKKmJLEDRkaqEJP4VJxmBhz\nLOGWnZjFhfKmBjUNShVlwo4HHy8s91Oud7Df0YRZsz2nriwUXgoMopPUNIj8QjZW98mH5EmeWjzN\nblM1rXkoAqNRL0vpMPuMTUXL6ONJL3vsVdRazlXzyWyaZ2f6mIos4tLZ2G9pZjLhI5yJ8769RyjR\nbKwaeIPLPDnWz1w0BMBjQ+NIgFmvx6wz4DDYqLNXYNGXYNEZCCSTg44dAAAgAElEQVRjTAYWeWpk\nkl8MT1CiUdNUVkqr20VbRRkOo4GHeoaIpNJ8+OjhovfVt8Loop+5cISmUjeeoJ9/OPEcv334AI1l\na7cZzsfEUoDnJ6b4zaPVec0J3w58Ph8ej4fOzs4LBgxdDtDpdLjdbtzuFWUmnU4zPDxMIBBAp9PR\n19e3rbY2RVH4u7/7O5577jkef/zxXHZ7MdBoNHz1q1/lrW99K7Isc9ddd9HR0VH0cS8riMs77EWS\npFrg3wA3K9k03xBC/EMhx7piSXwVc3NzjI2N0dTUdMlX9BdXiFlZ4U/u70WRJezCwlmGkRSJygUb\nxuQ5MpJVCsuuGBaMVFC441pBYZxp9GioUTZ+rGZhpD2zm3nVMrOpBX4xf4qDjmZqjZtLxudjIDRJ\nOBOnnd1opfzfZhbJxH7RwhQ+xmIzeBMLtFt3s8voXrfCjmTiDEYmVtzouiKem/Nk9KOVK1PHsorM\n0LKXs4vjpJUsbeZ6dhuqCWajjMe9dFbUsrt07fMohGBieZGTU6N4wwEkQK/W8PaWAzgMZiy6zeeE\nH67eTTqbZTq0xERgAc/yIj2+BQAchhICiSTX766nxr6z5HgxUtksPzzTS6nRxDvbDxJKxHmo/yW+\n8dyLvKOjhRsa69fPA5dl7u/uwW3R8Ue/tnNKwaohLJlMcvjw4R1XynYasiwzNDSEVqvl+PHjuZjV\nfNva4vE4H//4xykrK+OnP/3pju7333bbbdx22207drzLDQKBcnnL6VngU0KI05IkWYCXJEl6TAjR\nv90DXd6fgkuIdDpNX99KlvaRI0fWTUe61PjGM5OcnQljxcQEsxiTWsoWLWjkC13wfmcURRIrxrAi\nZPQZFomTojm7CzWbO+0lJCqUUpyKlXGNl1PLgwTTUfbatnZ9L6VCjEancVOKQ9r+yEStpKGRWtyi\nlHHFy8vBITxxH/tsey6Q2BUhOB0cRC2p6SjajX5ORtdIagaXpzm7OE4sk8Kls9FubcCqNSMLhbOR\nYcz6Et7UeKGsqQjB8KKPk9OjLEQjmDR6qowuZuN+3tq8nwZH/otEnUZDY6mbxlL3isExEWN8aY5f\neUcB6Jn1sdtVSntF/gur7eLRgSGCiQQfOnAtGpWaUpOF3zp4nEeGzvCj3kGmAkE+cLBzTZzsE8Nj\nzEdi/MlRI2dfehGr1Vr0SNF0Ok1PTw9Op/MCQ9jlimQyydmzZ6mqqrog7nWrtrZ4PM7XvvY1Ojo6\neOSRR/joRz/Kxz/+8cv+8V52EJd32IsQwgf4Xvl3RJKkAaAauEri+WJqagq3272hu1OSJBRFuWQZ\nxb2zYb7y5DhqVISJ4QgYcYSMa0g6qcsQNaeowY2RwmYWAyRIMsM8TsWKXeRvhNKhpTlbx5Rq7hXj\nWYwjpW0bzhnPKjIvB4bQSzrqRf6RnOvBLBnpFE0sEsCTmeXE4mnqTZW0WxrQqbWMRqcJpCPsNzUX\nFeoSykaZSHpptFeSzKb54egzRNJJnFoLnfYmXLpz+/nDsSki2QS/0XYU/Ssyuqwo9M17eWF6jEAi\njlVn5GhZG6V6G4/NvkCjs5xGZ+FkK0kSpUYzI0uCrKJwfW0rA0te/u2Fl2ivcHN7Z3ve+9T5YnJp\nmecnPByqrqf6vKEteo2Wd7d38cL0GE9PDDEfifI7Rw/hMq/I2r5QhCeHx3lXp5v/623t644UtVgs\nucozn97r1RG/TU1NuaCWyxnBYJCBgQFaW1txODYPCbq4rU1RFDweD9/85jcxmUx8/etf58knn+QP\n/uAPuOWWW16lR/D6x8oUs8u6Es9BkqR64CBQUJ/fFUviTU1Nm/Zsr5rQLgWJJ9JZ7v73bhQBGkVQ\ntWDDkFyfhCKWJGpUVFO44xpgkllUqNglb78lRYWKeqUKozDgwcdTC6c5VroXq3btfmR/eIJINkEH\njWvCagqBJEmU48QpbEwxhyfmYzaxSL2pitHo9Eo2urbwfUJFKPTGR9CpNSzGg4wFfdi1Zo7aOijT\n2S8gmGAmkpPRG5wrr8fQoo8nR/uIpFM49GauK99LtakMlSTxzNxZJCRu3l38fmMwEeNF7xh7nBUc\nqGyg011H99wEL86O8qUnf8mtrc1c11C/I61mmVfkcHuJgRsaWtb8XJIkju3aQ7nZxk8GX+Yfn3qO\nD3Xtp8Vdxg+6e7CUaLjnrSsO/PVGiq6S+sjICIlEApPJlKvUL54TPjMzg9frZf/+/RiNly5rf6cw\nOzuL1+vlwIED2058E0LwwAMP8M///M9873vfo6mpCSEEw8PDVyvx7UKAeG0rcZckSafO+/4bQohv\nXPxLkiSZgfuBPxJChAs50RVL4lthNbVtJ/ehYOUG+NePDuOPpdGn1VTM2dEo6y8UFEkQM6dwYt9S\n/t4MKdIEiFAlu9BR+OMpFw4MWT1jTPHUwmm6nG1UGc5VRovJIGPRGSpxYZd2tu1JI6nZTTVu4WRc\nmWY4MgWALGQ8KR9OjRWL2pT3zU4RCjElwXB8ioicAEAv6Thsa8Otc645jiwUzkZHVtzojW0ksxke\nH+llYGEWp97CjRWtVBjO/d1MzM9M3M/1dS1Y9cVVyUIITkz0o5Ikrt+1IuGrVSq6qhrZ46zkKU8f\nP+4d4OXpGd6zv7PovfLHh0ZYjMV4/75j6DYIugFocJbx4UPX81DfS3zrVy/RXO5iKhDib9/TjsO4\n/qJUkiSsVitWq5W6urpN54QHg0EkScoFolzOEELkFiVdXV3bvl5Zlvnrv/5ruru7efzxx3PJkJIk\n0dKydiF1FVvhNW8x8wshDm/2C5IkaVkh8P8QQjxQ6ImuWBLf6ma/3dnf+cITgftemsUU0+FetG66\nxx0zppAlQTnFhc0sEgDApWwu7eUDizDSnmlkVDPFyaU+Wi11tFrryAqZl4ODGCU9daLwiWpbwSQZ\nsAkLYeKYZSMRYixmgwBoJTU2tQWHxopTa8WmXmnliSkJonKCqBwnKseJKXFicjKXNq+R1HRa9lCl\n37idbjQ2TTgT5717DzMXCfHIYDfRdIq9jgba7HWozhsck1VkupeHcRnNHKoqfkLZ2PI8E4FFjte2\nYtZduKViKzHyrubDjC7P8czUAF/75bNct7uet7Q2oy/A+OUNBvnl6DidFbXUO7aWrm0lRj504Dp+\nMvgyIwvzXN/o5B1789/7Xy9QJRAI5LpFhBC5cBSHw1FwStqlxGq/ut1uZ9++jcfAboRYLMbdd99N\nXV0dDz/88GVv2Hs94HJPbJNW3iT/AgwIIf53Mce6+m7ZAOfnp+8UMrLC/zmTRKOoKPNbtjSpRS1J\nSiQdVlF4G41AsCgtY1WMlBTRmnY+dGhpzTYwqfYxGPEQykTRqjTEsik62YN6B2T0jRAVcbzMUypb\n2Z2tgSykyBBVxYmo4sREHH82CElQISFYeQ5WYUCHXtbjFiaWNSEklcRNjkObhsuEMlFG49O0lVUx\nGfBzemYSm87Im6sP49SvNe71ByeJZpK8veWaolvAMnKWpyb6cRnN7HPXrfs7kiTRVFrJLpuL573D\nPDc+Se/sHHd0HaChNP8FoKwo3N/dg0mn5+bG/HuRNSoV6WyWEq2az7+zuGjVUCjE0NAQ7e3tOJ1O\nhBAkEok1KWnnk/prOVs7FovR09NTcL+61+vlwx/+MB/72Mf46Ec/etktUF7PeI3l9K1wHPgw0CNJ\nUvcr//dZIcRPt3ugqyS+AS5FJf7NZzx4ozIVi1bUYot4RrVMvCRDrXAX5UiPECMh0lTIO2sIUqGi\nQa7CKEqYSs4BUI4Tq3TpJqEpQmFUmkIrNOzKnqv29WjRKzZKFRtkIUOWqCpOVEogAQZRgkHoKRE6\nVKw879PqedJkOWrp2JTAlVdk9BKtFl8kSDAZp8lawz5n47qjScPpGEOhKdrLq6mxFR/X+6vpUcKp\nJO9tO7blgkCv0XJzfQetriqeGD/L/3nuJLd3tnNN/frkfzF+OTqOLxzh1zu6Nu19vxi98148wSX+\n123NVNkKM18KIfB6vfh8Pg4ePJgbuylJEkajEaPRmEsVWyV1r9dLJBJBp9PlSD2f6NOdwmqgS6F5\n7SdPnuSTn/wkX/nKV7jpppsuwRVeuViZYrbzSupOQQjxDBRxYz8PVyyJb2eS2U5gbDHGV0+MY47p\nMCW2nlscMScBKCtSSl8ggBoVTrH9Vq+tICFRpjiYU/tJiyxLUgCXsBfUVpYPppgjJpI0ZWrRbOIR\n0KLBoVhxsP51RKU485oldpW4KddvvsUwEpsmlIkBIAkVN1UcoMK48WvSH/SgVam5ob41j0e0OZbi\nEU7PTtDqqqbKkv/7oMLs4Dfar+PnY908eLYPXyjMuzo71iS/nY/FaJQnhkdpdlXQ5Mrf/BhNJTkx\n1s+hWhsf6CqsG0GWZQYHBwHy2k9eTUmrqlo5XzKZJBAI5KJPtVptzv1us9l2fD9dCIHH42FpaYlD\nhw5tuz1VCMG9997L17/+dR566CEaGorfcrmKtbicW8x2ElcsiW+FnazEFUXwPx/sR8hQurT1il0g\niFlT2DAXJYHLyCwTxKFYizLGbYZZ1SJpsrgWzESdSfq14+wSldRQvqPSYETEmGUBl2zHrhRumlNQ\nmNTNYlDraTNvfvOcSy4xEl/JmK4zuzlU2rxp1Z5RsszEF2gvr8Go3XqhthVOjPejU6s5Xrt9Y5Ne\no+UdzYf5lXeYk55x5iNRfuvwISwla69LEYIHunvQqtTc0rQ9J/0To73IQuGvbm8tyBmfSCTo6emh\nsrKSmpqagt4zJSUlVFZW5qJPU6kUwWCQhYUFRkZGUKlUuUr94jzz7UKWZQYGBlCr1Wvmlef793/x\nF3/B0NAQTzzxRMET165iC4jLPuxlx3CVxDfATlbi33l2jJe9IcqWLBs60c9HUp8hrZapK7IKXyJE\nFgWXUviwlM0QJ8mc2o85oscSK8EU1+MvizJl9hEjTpPYtSP74/IrMrpeaNmVLS7cxKteIEGaY5a9\nG8a5CiHwJHz0RscBOOJqZbd16ypzOrpAVlFoL88vZnYzLMejTIWWuLamGUOBCwKVJHFdbQsuo4Vf\nTPTw1aef5cNHDlFjv/D98IJnionlAG9r2bfGOLcZhhZ9DPvn+b9v2V3QhLLl5WWGhoZoa2vLubF3\nAnq9fk30aTAYzMnfq73Zq6Ser5EsmUzS09NDRUXFBaM880UkEuFjH/sYbW1t/PCHP7zsHfevZwgu\n+z3xHcMVS+L5uNNTqVRR5xBCcKp/jC/9YhJjUoslmt/NOGJJokGFk+JahRZZxoAOi7gEIyAReDSz\nqBUVzqUV451KSJQtmNGn1CyVhkgyQotowCAVV5V6mCUuUrSk64pSFCJSnHnNMnWGCsp065NGSklz\nJjzCQnrF0X+wtCkvAgeYjPooNZqoMBcfh9q/OIMEtLqKny7VXFqFo8TEI6On+ednfsX7DnRysGbl\nuKFEgkf6B6mzl7LXnf/iI5FJ84vRXtoqzNx57fYIbVWO9vv9HDp0aMv88GKh0+koLy/PGc8ymQzB\nYJDl5WXGx1cWaueT+nptpauBMy0tLQWNJvZ4PHzkIx/hE5/4BB/5yEeuGtguNQSXpLvocsQVS+Jb\nQaPREIvFCv77RCJBb28v//hyiowi4c7DjQ6gSAoxU5oyHKgp3KCTJEWIGNVyeVHGuI2woAoQkRKU\nLZpRn6cuSEjYQkZ0aQ1+d4SzqiGaRX3B++QhEcWHn3LZUZRLX0bBo5vFpNbTZlpfRp9PLXM2Mkxa\nyaJCwlVio8maH7FFMnEWkyGuryvOnQ0r8vbggpddtjJM26iMN0OZycb726/jkdGX+f7pM/hCYd7a\n1sKDZ/tQFMFbmrfXGvXk2ACJbIa/un3fpnvtF0OWZfr6+tDpdBw6dOg1cZZrtVrKysooK1sJ7Mlm\nswSDQQKBAJOTkyiKcgGpLy0tMTU1VVCAC8Czzz7Lpz71Kf7pn/6J48eP7/TDuYp18DrITt8xXCXx\nDaBWqwuS04UQzM7OMjk5ib68nhdmBnAGjGiz+VWQUVMKRRI7YmgDLomUnibDjHoeQ0KLaQN1wZDQ\nUeG1s1gZpl87Tp2opHqb++SykBmTpjAIHTVFyugzr8jo11j2rnGVy0KmPzqBJzGHQdFhkY1EdQm6\nXPkT8mTEhwS0lRVfOU8F/UTSKY7v2tkZzwatnne3HOWZqQF+OTbB8IKfuUiEm3e3YTfkr9ZMLC/S\nN+/l7uvraKvIf083Ho/T09NDbW1tzpR2OUCj0eByuXKRrrIs50h9cHAQWZZxu92EQiFUKlXeyoEQ\ngu9+97v867/+Kz/+8Y/ZtWvnZ6pfxQYQrJkY+UbFFUvi+bjTtyvHrA5V0Wg0HDt2jP/v8ZWxk9ZI\n/qv3qCW5IoGzclMVCDJkSZIiQZokKTSosWHGhGHdKlsg8EvL2BQT+iIS2jaCR+1DEYLSRfOmVb42\nq6bCa8dfFsFj9hElTqOozXuqmQcfCZGmNV1XlCoRkWLMa5apN1RekIMOK1Gq3eEhonKSspQdS9bI\nuGmWdlsdVl1+lb8iBJ7oHHWOMsz64ivn/gUvJRoNDfadn6qnVqm4qb4Dm97EM9MDqCWJWnv+sbVp\nOcvjIz3UO438/o35ta7BSjvWyMgIHR0dWK2Xpnthp6BWq7FarUxNTVFdXU1dXR3hcJhAIMDMzExu\n8tj5Q10uRjab5c/+7M/wer088cQTl93I1Dc6Virxq3L6Gx7nzxS/GNs1ti0uLjI8PMyePXtwu92k\nszIPdvswxnUXyM2bIanLkNBnsWJiGA8pUiRIIZ8XVqKWQH7lW52kwSrM2LBgx5ybMx4mSlJkqJJ3\nngQCUoSAKoJjOT91YWWf3IIulWDZGSIkRdglKqlg43Q0gJCIrMjoWSeWomV0Hya1nlZTfe7/hRCM\nxr0MxzxohZrGeDUmuYQRyzQWbQlt9voNj3kxFhIBYtkUN++AoS2ZzTC6PE+7qwb1On3oO4VwOg6A\nVqXm3u7neGvLPtrKt678n50cJphM8I8fPIhes/X1CSGYmJggEAjQ1dX1mkwL3C5WA1waGhpy5rj1\nJo+tJsul02ksFguyLFNSUoLb7eauu+7i8OHD3HfffTtuYLvrrrv48Y9/THl5Ob29vcCKSfCDH/wg\nk5OT1NfXc9999205fOUNjdc+O/1VwxVN4psh3xazbDbL0NAQqVSKw4cPo9PpkGWZp4YWCCQyVES2\nrjpkSSFkSxCyrdxYo8RwGVS0OHS0VldRX2qk1q7Hrsmgy0SZml+mb0lmJKLhzHyUscRK7KhR0mMT\nFmIkVoxxO9wbLhDMaObQZ9TYgvmrCxIS9pARY1zHsivGuGGGBZZoEDXrhsOsyOjTKzJ6kQuRi2V0\nIQRz6SVGYlOEs3HsGTM1iXI0qJnTLZOQ0txYun/dIJeNMBH1UaLRsttZ/KJp2O9DVhRaXcUvCDaC\nPx6mZ97DHms1HY4Gnpvv4ccD3fjCIW5ubL0gQvZ8zEWCvOSd4ANdVRyu23qbJpvN0tvbi9FoLKgd\n67XA0tJSTjHYqP3r/MljDQ0NuUltJ06c4Mtf/jLj4+O0tbVRV1fHxMQEjY2NO2pku/POO3MGuVV8\n8Ytf5JZbbuGee+7hi1/8Il/84hf5m7/5mx075+sP4qqx7UpHPpV4MBikv7+fXbt25dKkFEVBURR+\neGYeraLCmNi48lAkQciaIGyPk5UEt7a6eE+rCU10nr3tG7fdtLbAmzIZAoEAy8vL9HoDDCwLhkIS\nvQtLpGWBFjURKY5N7FyCWkxKECeNK7i5jL4RdBkNbp+VuClNwBWjRz1KmXBQTxU66ZzsP7ljMvo5\nN3qp1sZ8apnhmIdQNkaJoqU+WYEtu/JYUlKGhZJlakxlVBq3Iy9nmIktstddsy3i3wj9C9OUGs2U\nmy6N5CyE4KnJPvRqLZ3ORvRqLTdXHaJ7aYSXZiZYiIZ4V/shTLoL931lReFnQ2ex6iTeUZNhbm4O\nh8Ox4f5wNBqlt7eX+vr6Dcf9Xk4QQjA9Pc3CwsK2A1xWJ7U5HA4SiQQPP/wwer2ep556ik9/+tN8\n5StfKaglbSPceOONTE5OXvB/Dz30ECdOnADgd37nd7j55puvaBIXVyvxKwObyembVeKKojA2Nsby\n8jIHDhzAaDQixMrKTwhBIJ7hxPAS5kjJumSnSIKwJUHYniCjUrhxj5M/uL4WAtNo1Alajh7ZsndV\nq9Xm2mZaW1cCLgKBAHOLSzw3HuC+YZmhhIdSxUat7C5qetkqFqUgKiFhihYuiUpImGJ6DHEdQXsc\nvz1AQApRKyqopIwQUebw4y5SRldecaMb1XpcWjvPBs8QzETRCw27km4cmQu7BWYMC6gkiYOlzds6\nz3RsAVnsTG/4UjyKLxLieG3rJWtBGvTP4IsGOVrWhv6V4Bq1pKLL1YJTb+XU4iDfPf0M727votJ6\nbhF5yjvBQizCP7y/g6ZKHcvLyxfsDzudzhypLywsMD4+XnAc6asNRVEYGBhAkqSCHPNCCL71rW9x\n77338sgjj+QW9IcOHeKP//iPL8Ulr8H8/Hwu7KaiooL5+flX5byXLQQo2auV+BWNjW6iqxVGeXk5\nR48eBVbcrIqiIEkSKpWKn/QuIAuBJXqh4UUgCFuShBxxMiqFY/V2Pvmm3dQaswwPD9HY2FjQEAVY\nCbioqKigoqKCA53wm5EY/3RilP/sXiakilAtuylXHAW3mykoBNQhjBEdqi1y3/OBSkg4AyYs0RKW\nXVEmDLPMs0QWGQM6qouW0RdJkMaCgZfCg+iFhtpkOc7M2slxKSlDWBOnw96AUbO9nuXJqA+X0Yx7\nJ3rDF7yoJInm0kvj3E5lMzzvHcRVYqXBsnbSXIOlErvOzLPzZ/le93O8uWkv+yp3EYjHeM4zzJtb\ny7i1beV1WVWJVveHV0k9Go2iUqloaGh4Xex/p1Ipzp49i9vtpra2dtuLp0wmwz333EMgEOCxxx67\nLGaeS5J0xfehi6ty+lVcjNWACp/Pl3PYnl99r35whBDc/7KPkrQGfebc05vSZVgsj5DSyByosfJH\nv7abrloro6OjTPnjOx56YbeY+B/v2s8d18b5wk+GeMHjY0kVoC5bhYnt97ouS2GyKJgjOxvMoc2o\nKfdZiRvT+MsjKCpQAaPaaSyKEYtiwiRKcoNLNkOWLAkpTVAVYU6zBKwQV02yDGfGhmqDBcyyLgzA\n7nWIbTOE0zH8yTA31K9fOcuKQjSdRCVJWLaYKa4IweDiDLtsrjVS9k7hV94REpkM17sPbHiTd+gt\n3Fp9lOfne/nZcA+z4SDBRIwSrYrPvb1pze+v7g+bTCaCwSBVVVW4XC4CgQC9vb3rVuqXC8LhMH19\nfQUHuAQCAe68805uvPFGvva1r72me/5utxufz0dlZSU+n6/gYuANAwHiaovZGx/5rlZX4xYtFgtH\njx5FpVLlqm/ggg/vwFyUkcUYrsjKXrRAELIkCJTGKDXp+IvbO7hxj5NoNMqpU6eoqqqiubn5kq2c\nG1xGvv2RA/y4d54vPjpKf2KcctlJjVK+rfSzJVUQrayiJLnzLWsSEpqsGkUCfUSFJq0maUkQ1sWA\nRVRImBRDjtT1QkdKSpGQ0iRUKZJSipQqRZoLV96VyVLK0vZNFwACQUgfocLgwKjZXnvYaHglVU2r\nUvOid4xoOkkklSSaThJNJ4il07nfLTWaqLeX0+Aop8rqWDORbCroJ5pOcf2uS2NoW4yF6F3wsMda\ns+741POhV2u5sfIAPctj9Mx5APjCO1sot6xPwJFIhL6+vgvGca46oy+u1C8XUp+bm8Pj8bB///6C\nquehoSE++tGP8tnPfpb3ve99r3nle/vtt/Od73yHe+65h+985zu8+93vfk2v57XH1Razq3gFs7Oz\nTExM0NraSmlpaa76VhQFlUq15sP7QLcPFWCO6ZFVCouuCDFjmpuaSvnrd7dhM2jweDwsLCzQ0dGB\n2XzpRneuQpIk3tVZwY17SvnyL8a576VZguow9dnqvIxvKdKEVDHsgfX70ouFQLBUHkWjSJR6DagU\nCeZAVgvSRpmUUSZtTjKrj4PGf8HfqhUJTUpCk1RhSOnI6BXijiz18Qrs2a33Y6PqBEky1G+jCo9k\n4gwGp5iIzCKAX4z3AWDQSJSZtNSXllDjLKXCqqfCWkI0leWpkSVOeSZ5aXYCvVpNrd1Fg6OcevtK\nb3nfvBeDRntJesOFEDzl6X/FzLY7r79RSRKt9jrGwl7aq0y87+D6z4/P58Pj8dDZ2bluL/T5Tm54\n7UldCMHY2BjRaJSurq68c9PPxxNPPMHnPvc5vv3tb3Po0KFLcJWb40Mf+hAnTpzA7/dTU1PDF77w\nBe655x4+8IEP8C//8i/U1dVx3333verXdVnhCjK2SRsZuzbAG+pZyWazG+6bpNNpnn76aVwuF+3t\n7Wg0mpzzHNbfd0pnFW74+2cRy2qs4RIW3REUjeAztzby20drSKVS9PX1YbVaaWxsfM3ktzPeEJ97\neJBxf5wa2U2FUropOc+oFplRL1Az5cg7eW47CFkTLLtiOKf1GMObzPZWCVJGGVkr0KQltCkVqqyU\nu/asVmGhKYEla6Qhkd++sqdkjlhJnHftun5Ld/lyKsxA0IM3tohWreJ9Byu4paXsFbLWo1LOdQxE\nIhFKSkpy/cVms5l4RuZXEwF+ObLMUyNLLERWsvldRjNL8ShtZTX8WkNnns9a/vAEF/nR8CmOlLXR\nmGcOPMCpxUHGI7Pc/3uHaXFfuNhTFIWRkRGSySQdHR0FkeHqcVZJPRAIXFJSX215M5vNBbV9CSH4\n+te/zoMPPsh99933unDdX4Z4VSQLSZIeBVyvxrk2gF8I8bZX40RXdCW+0YfY7/czNDRESUkJra2t\nFxD4ZqaRJ4f9RFJZzIoaX2WIKlsJX37/XjqqLMzNzeUq+tc6hGF/jY17f7eLzz44wGOD88SlJA1y\n1bqys0CwpA5gSGovCYFn1TLB0jglUTWG8OZvR5UiYYhuMDZH5CwAACAASURBVHkMQbAyBRJUJ8vy\nOreMTFgXpc5UuSGBCyGYTwQYDHmYTwQw6zT83vV1/PbRGlzmi41bmtycayEEiUSC5eVlJicniUaj\nGI1GmhwOjt1czZ/f1sToYpwTw4s8csaLPw5jgTmqLE5aSqt2VJ4d9M+gV2uot+RPOsupMGPhGX7r\naM0aAk+n0/T09OB0OoveCnq1KvXVyNe6urqCyDedTvPpT3+aVCrFz3/+83VT2q7i8sGrRaCXA65o\nEr8YsiwzNDREIpGgq6uLwcFBMplMrmLeyvV576kZJAFRS4p37C3nz9/Rgl4l6OnpQZIkDh8+vO6E\npNcCJp2GL71/L9942sM/npggpUrTmKldE9MaleIkyeAKXxrZf8kVAwT2WX1RUn3SIpO0yFQlXehE\nfs9xUBtFRqzr1FaEwBtbYCjkYTkVxWXS8ek3N/KBrirM+q0/NpIkYTQaMRqN1NTUIIQgHo/nJmfF\nYjH0ej1txLj1HTWkDS7+/CfDPD5+liH/DDfVd2AvKT6qM5XNMB6YZ7elCvUGIS4XQwjBaf8QdqOW\nT9xcf8HPVqd5NTU15bLGdxKXgtSXlpYYHh4uOPLV7/dz55138pa3vIXPfOYzr4vQmqu4cnCVxF9B\nKBSir6+Pmpoa2tragJVe8ampKSoqKrBarZsSeFpW6JuNoFLBF97Vynv2V6w4dIeHL9vAC5Uk8fs3\n1tPsNvOZB/oZYJzGbM0F/dmLqiBqsdLbvdOIGVPETWms8zo0mcJvjIpKEKpKYVR0lKXzH/gS0IWx\n6oyUXmT0WkwEObU0QDidoM5p4I9ubeH2fRXoNIVfoyRJmEwmTCYTtbW1+Hw+xsfHqaioIBwOE5+b\n438cMfF8XTnfPLXEvb3PcLiqkYMVu9eY4LaDkWUfslDWXahshImID38yzP/77lasJecWRDMzM3i9\n3oLNYIWgGFJfDXCZn58vuPujv7+fj33sY3z+85+/aha7issSV/SeuKIopFIpxsfHWVpaYu/evZhM\nppx5LZ1O4/f7CQQCRCIRjEYjTqeT0tJSDAbDGlIPxNPMh1M0l5sYGxsjHA7T0dHxupDeRhYi3P3d\nbuZjWeqylf9/e2ceHVWdpv+nUqnsS6Wy7wlJCNlDEiAggRQM4Di0trj8xlGIIjK24kB77G4RHUE8\nSrfKYre23QcRkd22G22hcZKwE7awZt9DyJ7UkkrtVffe3x/0vZ1AgKJyK1VFvp9z/AOO1H1rfe73\nXZ4XIYwEFChcEdXBU+WG4H5+TTtoAYPOGAUEFBDcMLqGOWWoAeogE5I0UfCmLBufMwiMqPG9jkzJ\nBM4nnaIpVCiaUTdwA5FiD7zxbwn4t0nBELrwl9qmaRr19fUwGAzDaskMw2BwcBAKhQJNnf3YflWN\n8l4aEk9vFMalI8LXuq12f6kqg95kxoKoaRalvY2UCYfaz2BSmCd2vpADF4EANE2jrq4OZrMZqamp\nvHuBj4Y71dTZFaIuLi5ISUmx6vR8+PBhvPfee9ixYwcyMzNtEP24ZHwPsNuAcS3iarUaly5dQlBQ\nEOLj4yH45w/WSLVvhmGg0Wggl8shl8uh0+m4E4BEIuHu8tVqNaqrqxEaGoqYmBi7j55YgkajQVVV\nFbwDgrD5nAqnmxUIoQLgxXig1bUL4R3+8DDwWwaQSzQYEOsQ3OwJd531omD0oNA3QQeJyQ/ResvX\nlXa596PXXYGFMQ/By9UdcoMK5/uqMWDU4v/lRuCNeQnwduM3UcWOKoaEhNzzs0HTNP5xtR2/Lb2O\nfq0ZacHRmB6dDA9Xy98HuU6N3RUnkR2YiEliyzaOXeyrQ9NgO759KQ8pYb73FbMjQNM0ZDIZamtr\n4eLiwm0ku5/0O03T+MMf/oDDhw9j//79ZOaaXxz7A+SEjOt0uqurKyZNmgR/f/8RjVuGIhAI4OPj\nAx8fH8TExAw7AVRUVICiKAiFQuj1eqSnp9/R99yRYBgGXV1daGtrQ2pqKvz8/PBFAoPNR5rxZVkb\nhHCBm9kF7gZ+Pya0gMGgvx5eStdRCTgAqMKNcBUIEa63vD7LgIHSfRBhnhJ4CEWolDejWnkdQT5u\n+POTmZiZaLl3uqWwddmUlDt74g/FxcUF/zE5BoVpEfjsWCt2nLuBVmUPCuPSER9g2c1KbX8HBBAg\n1seyUo7CMIhGVTuemRKJlDBfKJVK1NTUWG2GYg80Gg0aGxuRmpqKwMDA+66pGwwGrFq1CkKhED/9\n9JPNR942bdqErVu3QiAQICMjA1999ZVTZO4IjsO4PokzDAODwXDP0bF7YTAYUFlZCaFQCE9PTwwM\nDEAgEHCndH9/f4drhjGZTNxpJTk5+bYRoYOVPXjrQA1oMxDa6Qd3I38n8UEfPfpD1Ahu8YS71noR\nN7lT6EnUIUIfhBCj5R3/g0INmrw7kSVJwA1ND+QGNX6WEYq3Hk6Cvye/GQeGYdDc3AylUomMjAyr\nrUiruwbx9g+1qO1RY1pkEvIi7j4iRTMMdlw9Cj9XH8wKz7boGkc7L8EANf6xYipU/T3o6upCZmam\n04hKT08PWlpa7jizDoycftfr9aivr0deXh7eeust/PznP8eqVats/p3t6OjAzJkzUV1dDU9PTzz9\n9NN45JFH8Pzzz9v0unaGnMR5ZlyfxHt7e0FRFHx9fUc0brH0MZqamjBx4kQEBv7rBGc0Gm8uJOnu\nRl1dHdzc3BAYGMjNDNszLalUKlFbW3vXhrv/SA9FfKAXXt1bgW6XAUh6fW7zgrcWja8BIpML3LSj\n+5HUiM0QAJCY7q/jWOamglDgggp5M/w8XbHlqXTMS7FsLO1+MBqNqKyshJ+fH3Jyckb1nqeG+2L3\n0hy8+2Md/l7RgH6tCnMnZMJNOPJX+MbATQe4rADLFroMmrTo0SmwUhqH9uYGAEBubq5D1b/vBHuj\npFKpkJube9cJkJEa5RoaGvDdd99h06ZNEIlEqKurw759+7BgwQKbZyDMZjN0Oh1EIhG0Wi0iImzj\nm094cBnXIn7x4kWsW7cOLi4umDVrFqRSKaZNm2ZRCo3dI05R1IijY25ubggNDUVo6M3U560zw97e\n3sOa5MYChmHQ0tICuVyOrKyse143NdwX3y3Pwy//UoULUMLoboZE5j2qJjSTKwWdpwl+vW6jehwG\nDPQSM/xM3nBlLBcancAApUgNMMDc5CCsXZiMQG/+F3Wwo1iJiYkIDubnBsFDJMSGn6cgJcwHH5c0\n4a81Z/BIUi783G/vFGdnwyO8LSsztAx2QSAA4pge+PlFIioqyuHr38DN72FVVRW8vLyQnX1nT/g7\nIRAIUF9fj0uXLuEf//gHEhMTUV5ejmPHjqGtrc2mIh4ZGYk33ngDMTEx8PT0xPz58zF//nybXY/w\nYDKu0+nATWGTyWQ4cuQISktLcfbsWYSFhaGwsBBSqRRpaWm3nUbYk2xMTAzCw8Otcn5Sq9Vck5xe\nr4e/vz+XfrfF9ie9Xo+qqiqIxWLEx8ffV6rQTNP4uLgJO861w1MvQnC3L4S0dadohVgLZYAWYQ1e\noxor0/mYIYvVI14bDn/zvWfYGTCQi1To9OyHmyuwcs4ELJ7Gv1CxY03d3d3IyMiw2Q1aWZMcv/xL\nFcyUAAsSJyPK719ZIL3ZhK8uH8EE3wjkBidbFPOPbacR72/Cn5/Ncop+DuDmjfG1a9e47+H9QtM0\nNm7ciBMnTmDv3r02mXu/GwqFAk888QT27dsHsViMp556Ck8++SSee+65MY1jjHH8O0MnY9yL+K2w\np9WSkhKUlJSguroaKSkpkEqleOihh/DFF18gOzsbTz75JG8/0GydTiaTQS6Xg6ZpBAQEcM03o01p\nsin/0brF/XCtG+/8UAuBSYCgLj+4G+8vkcOAQWesAi56AYJaR/fayaJ1oPyAFFX8PU/0JoEZ7R69\nGBBpMCVWjA9/noIIf/7rvGazGdXV1RCJREhOTrZ5TfW6XItX91agVabDQ9GTkBkaC4FAgMreNhxr\nrcL8qCn3XHYCAN1aOY51XcYbMwLweG6sQ/Zw3IpcLkddXR1SU1Ph73//a2B1Oh1WrFgBf39/fPrp\np3ZZm/rtt9/i8OHD+PLLLwEAO3bswNmzZ/H555+PeSxjCBFxniEifg8oisK1a9ewZ88ebNu2DYmJ\niUhLS8OcOXMwe/ZsBAQE8H6aM5vNUCqVkMlkUCqVEAqF3Cndz8/P4h9YiqJQX18Po9GI1NRUXtzi\nKjtVWLG3Av1qEwJ7vOGjsVwMdR5GdEeoIGl3h9eA9bFQQgbdyRoEGcWINNw9VT3gqka7Vy8YFxqv\nz52AJfnRcLFBmlitVqOqqsrqU6G1aAxm/OZvNThS34+UoCgUxqXibzXnYDCbMT/SstnwMz1V6Df2\n4a+Lk6BWKTEwMACRSMTdSN7PZ24sYDMdmZmZVnWPd3d3Y/HixfjP//xPrFixwm5lg3PnzmHp0qW4\ncOECPD098fzzzyMvLw+vvfaaXeIZI4iI8wwRcQv48ccfsXbtWvzpT39Ceno6ysrKUFxcjGPHjoGi\nKBQUFEAqlSI/P98m6VOj0cil3gcGBuDh4cE1yXl7e4/4I8SKSmRkJCIjI3n9oZJpjFi1vxIXbwzA\nT+kBidyyOnlf8CB03kaE1nrBhbE+nkGJEQPhRiSrY+BJj/wjToFGp0cfZG4qxIlFWJ7phjAPGmKx\nmMtw8GWBy27ySk9PH5OtdLdCMww+O96KP55oRZCXD/q1amQHJmGSOOae/9ZEm/H99ZN4YnIY3v2P\nf6Xe9Xo9FAoFFAoFVCoV3NzcuNeNbQQda1jTGYqikJKSYlWG6vLly3jllVfw0UcfOUT9+d1338W+\nffvg6uqKyZMnY+vWrQ61c90GEBHnGSLiFtDd3Q0/P7/brCYZhoFSqcSxY8dQXFyMM2fOICAgAFKp\nFFKpFFlZWTbp7mU9uOVyOTQaDXx8fDhRd3d3R3t7Ozo7O2266tRE0fjt/zVi94UOeBhdEdDnfVdD\nGFpA40acAp4KIQK6RpfK7kvUwlUkQpJ6ZJHSCHW44dUDg8CEF2fEYEVhPNxcb+6AHxgY4MaLGIZB\nQEAA99/9vlesqJhMJm7TnT35v5pe/PqvNTDTDB4KzUSkBU1tTapOXOirwZ6lOciKunNaWqfTjbih\njRV1W59m2aUrQUFBVpnOMAyDv/3tb9i4cSP27NmD5OR79woQbAIRcZ4hIs4jDMOgvb0dxcXFKC0t\nxdWrVzFx4kSuSW7ChAk2aaQaHByEXC5Hf38/BgcH4e7ujvj4eAQFBdl84crh6l588I8G9GuM8FG5\nQyL3HrHpbdBXj/5gNS8Obb0JOkTqghFsGt6ARYNGj7scve4KhPm547ePpyIv9s5NWmazmTttKhQK\nuLi4WDzbr9PpUFlZidDQUERHRztMJ3d9jxqv7qtA14ABOYETkeB39yxMaUc5vL1MOPjqVIufA7uh\njRV1dkMbm36/U3bIWgYHB1FVVYXExESrms9omsaGDRtQXl6OPXv22H2L4DjHMb4oDxBExG0ITdOo\nqqriRP3GjRvIzc1FYWEhCgsLERQUxNuPHdvoM2HCBIhEottOmxKJBGKx2CaZAY3BjD+eaMXXZ9sh\noAF/mRd8VR7DUuxdEUrQQhrB9aP0SQ8zQBtoRqoqHq64+Vxo0Oh3G0C/hwJGUHg8OwyrFyRZtG1s\nKOxsP1u2cHNzG1YXZt+r/v5+NDQ0WOy+NtYM6Ez49V+rcbJJjnjfcOQFJUM4wqrVQZMWB9vO4PW5\nE7DsIctsWUeC3dDGvnYajQbe3t7ca+fl5WX157y3txfNzc13NXC5G1qtFi+//DIiIiKwceNGu2dL\nCETE+YaI+BhiNBpx9uxZlJSU4MiRIzAYDHjooYcglUoxY8YMq36kaJpGU1MTBgcHkZqaepu7Fnva\nlMvlUCqVcHV1HdYkx+eJqbFPg/cP1eP8deWwFLvJlUJ7jAJ+PW7w67e+C5gRMOiZpIUP5Y04Xfht\n4p0fH4BXZ8chN4YfYdXr9dzNkEqlgqenJyiKAkVRyMrKcujaJUUz+Ox4C744eR2B7r6YEZYJb9fh\nn41r8ibUKltRunIGQv34ey5D9wwoFApotVr4+Phwoj7S8qCRHqOlpYVzurMmo9TZ2YnnnnsOL7zw\nApYvX+4w2ZJxDnkTeIaIuB1RqVQ4fvw4iouLcfr0afj4+HCp95ycnHueGrRaLaqqqhAUFIS4uDiL\nfqQMBgNXT2eFia2nj+bExMIwDA5X9+LDw41cit2FFkDlr0d4vReE5lHMhvuaIYvRI04bBqOLmRPv\naXFirCiM5028R8JgMODatWtwdXWFUCjkTpvsDZElwmQPvjvXiPdL2iGAK6aHZiDU82YqmWEY/Hjj\nNCbHeOPPz2bZNIaRfBF8fX25mvqtzaAURaGyshKenp5ISkqy6nW9cOECXnvtNWzZsgVSqZSvp0IY\nPY73JXFyiIg7COwyEnY+/fLly4iPj+dEPSkpaViNtrOzE21tbUhJSbFqTpa95tAmOa1Wy/24SiSS\nUXlmD02xUwwDoUkA/253uGtcIKSsE/L+GB1MvgxcAJhAY1qcGK/Ojr9r3ZsP2EUgSUlJXE2WFSaF\nQgGZTAa9Xj9ssYa9/cYZhuEyND7hE7Dqu1q0ynTIDkzERP9o9OgUONZ1GZ88kYp/T7N8+xtfsalU\nKi5DZDAYuNfO09MT9fX1iIqKssqClGEY7N+/H5999hn27t2LxMREGzwDwiggIs4zRMQdFLbzma2n\nNzc3Izs7G/n5+fjhhx8glUrxyiuv8FrjY39cWVE3mUyjHslq6tNgY2kTyprkMFA3Pz5uRheI1EK4\na4QjijoDBpSIgdmNhsmdhtmdgcmdgtH75pKaqbE3T962Fm/Wfa2npwfp6el3HR+kaZprMBz62rEp\nZFs3GA7FZDKhoqICfn5+SEi4uShFYzBj9fe1KKntQ4xPKMAAcpMMJ9+YAXdX+/qjs2ZHnZ2d6O7u\nhru7O/eZux8HQ4qisH79elRXV2PXrl1W39wSbAoRcZ4hIu4kmEwm7NixA++88w4SExOhVqsxY8YM\nSKVSzJw5E76+vrxfkx3JkslkUCgUEAgEw5rkLJkVZjv2b3R0QhgUh4oePc63KnHxuhI6801RdjO6\nQKRxAe0CUB40zG406CFfdW+REPFBXkgI9sKjGaGYnsD/qtBbYd3X3NzcMHHixPuei6ZpGkqlcliD\nIXtDJBaLbdZgxXZyT5gw4bY92AzDYOvpNmw60gwBgKdzI4bNhtsTdiwyMzMTbm5uw0YBzWYzd0MU\nEBAwoqir1WosX74ciYmJ2LBhg80b2JRKJZYtW4bKykoIBAJs27YN06dPt+k1HxCIiPMMEXEn4fTp\n03jzzTexfft2JCQkQK1W48SJEyguLsbJkyfh4eHBdb3n5eXZxEbSZDINa5JjDUAkEsmIs8Imk2mY\nEA7tjDfTNKq71LjQqsD5ViUu3xiAn4cIiSFeiA/0QnyQN+IDPREf5I1Ab9GY1pvVajUqKysRGxvL\nm/sa68LHvnbsqtqAgACLb4juBWs6c69O7tNNcvQNGjElToxIsX3T/jRNo76+npu1H2l64tb5fpq+\nadqjVqsRGxsLnU6HxYsX4xe/+AWef/75MfmsFBUVoaCgAMuWLYPRaIRWq3XISQUHhIg4zxARdxLM\nZjMYhhkxLcswDHp7e7l6enl5OaKjo1FYWIg5c+Zg0qRJNnHYYru3WQMQLy8vrknOaDSitrYW8fHx\n3CY3Z6CrqwttbW02NcoB/jXOplAooFQqIRKJht0Q3c/7xa7T1Ov1SEtLc5oxKtbAJTAwELGxsRaL\nL0VRUCqV2L59O3bv3o2+vj7Mnz8fS5YswcyZM23umjcwMIDs7Gw0Nzc7ZDOjg0NeMJ4hIv4AQtM0\nGhsbuXp6fX09MjMzOVG3ZvPavWDHimQyGTo6OqDT6RAUFISQkBDOSc6RoSgKdXV1MJvNdnFfY21O\nh04NsCf1u+2fZ4VQIpFYPKHgCLDZjoSEBKtWtTIMg127duHLL7/E1q1b0dbWhqNHj+LChQsoLS21\n6ft35coVLF++HKmpqbh69Spyc3OxZcsWq0ZExyHO8QF1IoiIjwPMZjMuXbrEibpCoUB+fj6kUikK\nCgp4mxc3mUyoqqqCp6cnl/JnT+oURQ1rknOk06JOp0NFRQXCwsIcwn2NdUQbaq070jgbu7N8aNe8\nM9DX14empiarvebNZjPWrl2LlpYWfPPNN2PuV19eXo78/HycPn0a06ZNw8qVK+Hn54f169ePaRxO\nChFxniEiPg7RarU4deoUiouLceLECQiFQsyaNQtSqRRTp0616tTM7lgfqaEK+FcKlK1rsjVhSyxO\nbUlfXx8aGxutXmk5Fgw1T5HL5dDpdBAKhTAYDEhPT3caG1GGYdDa2gqFQmG1gYtKpcKLL76IrKws\nrF+/3iYOhPeiu7sb+fn5aG1tBQCcPHkSGzZswMGDB8c8FieEiDjPEBEf5zAMA5lMhtLSUpSWluLc\nuXMICwvjUu9paWl3FViGYXD9+nX09fXdcwxrKCNZnLL19Lulj/mCnaNWqVRIT0+3yz5pa6BpGrW1\ntdDr9RCLxVAoFDCZTPD39+eyHI74XCiKQlVVFdzd3W/zPLCUlpYWLFmyBL/85S/x7LPP2jVjUlBQ\ngK1btyI5ORlr166FRqPBRx99ZLd4nAgi4jxDRHwIhw8fxsqVK0FRFJYtW4Y333zT3iGNOQzDoLm5\nmWuSq6mpQWpqKreZbWi6WaPRoL6+Ht7e3khMTBzVaXpo+litVnPp48DAQN7Xu7J1ZLFYbJOlNLZC\nr9ejoqICISEhwzZ50TTNdW/L5XLQND1sO5u9Sxd6vR7Xrl3j1uJaw8mTJ/GrX/0Kf/7zn5Gfn89z\nhPfPlStXuM70CRMm4KuvvnKajIidcY4vmxNBRPyfUBSFiRMnori4GFFRUZgyZQr27NmD1NRUe4dm\nVyiKwtWrV7l6em9vL6ZOnYqIiAjs2bMHBw4cQGys9cszRmIkm072pHk/5h8joVAoUFtbi4kTJyIw\n0Pbz5nzBxp2cnAyJRHLX/3ekcTZ2vt/f339MU9Cs2521y2IYhsH27duxc+dO7N+/H9HR0TaIkjCG\nEBHnGSLi/+TMmTNYu3YtfvrpJwDAhx9+CABYvXq1PcNyOLRaLV577TWUlpYiNjYWer2eq6fn5+fb\nxG6UdfSSyWTDTpps+tgSUWIYBm1tbejt7UVGRobdbVEthTXL6e7utjruW+f7RzPOdj90dHSgo6MD\nmZmZVsVtNpvx1ltvoaenB9u3byfd3w8GRMR5xnFahO1MR0fHsLv8qKgonDt3zo4ROSbr1q1DaGgo\nGhsbIRQKoVAocOzYMfz973/HmjVrEBgYyPm9Z2Zm8nLqc3FxgVgshlgsRkJCAnfSlMlkaGpqglAo\nHLaZ7VZRMpvNXD02NzfXbk109wtFUaitrQUA5OTkWP1aikQihISEcA2H7BKc9vZ2qFQqeHh4cK8f\nH/0I7Ny6wWBAbm6uVXErlUq88MILyM/Px6effuo07xmBMNYQESfcF++///6wrmKJRIJFixZh0aJF\n3Gm3pKQEn332Ga5du4bk5GRO1OPj43mpP7u6uiIoKIgbqzIajZDL5ejs7ERNTQ08PDy4JjmaplFd\nXY24uDiEhYWN+tpjBTv2Fh4ejqioKF7r9u7u7ggPD+fc6Nh+hNbW1mH9CNZsZ2N92wMCAjBx4kSr\n4m5oaMDSpUvx61//Gk8//bTT9CwQCPaApNP/CUmn8w9N06isrOTq6e3t7cjLy4NUKsXs2bMRGBho\nkx9odjNbR0cH1Go1JBIJQkNDR72ZbayQy+Woq6uzuo48GkYaZ7N0sx1r4HKnMUNLOHr0KFavXo1t\n27YhLy/P2qdBcFzIHRnPEBH/J2azGRMnTkRpaSkiIyMxZcoU7N69G2lpafYO7YHBaDTizJkzKCkp\nwdGjR2EwGDBz5kxIpVLMmDEDXl5evFyHdV+jKAopKSnD1q0ajcZhTXJjuV3sXrDjev39/cjIyHAI\nl7tb14YOff2GjrON1sCFYRhs3boV3377Lfbv32/VGlKCU0BEnGeIiA/h0KFDWLVqFSiKwtKlS7Fm\nzRp7h/RAMzAwgOPHj6O4uBhlZWXw9fXlUu+TJ0+2ajRKq9WisrLyjmnokbaLDd3MZg/zEOBfc9TW\nbk0bK4aOsykUClAUBRcXF5jNZmRlZVl1I2YymfCrX/0KGo0GW7du5X2kkOBQEBHnGSLiDsaNGzew\nZMkS9PT0QCAQYPny5Vi5cqW9w7I5DMOgs7OTm0+/fPkyEhISOFG3ZA6dPQ2mpKRY7L5mNpuHdW67\nuroOa5Ibi3qsVqtFRUUFoqOjneoESlEUKisrwTAMvLy8rBpnk8vlKCoqwty5c/Hmm2867M0LgTeI\niPMMEXEHo6urC11dXcjJycHg4CByc3Nx4MCBcTevzjqTsfX0lpYWTJ48mRP1kJAQTmApikJzczPU\najXS0tJGNUfOdm6zi0i8vLw4Uffy8uJd1Pv7+9HQ0IC0tDT4+fnx+ti2hDVwiYiIQFRUFPf3I42z\nsaJ+6+RATU0Nli1bhnfeeQePP/74mDWwURSFvLw8REZG4scffxyTaxI4iIjzDBFxB+exxx7DihUr\nMG/ePHuHYldMJhPOnz+PkpISHDlyBGq1GjNmzEB2djY+//xzrFu3DlKplFchYBhmWD1dq9Va3ORl\nyWO3tLRwPuKOaJV6J9jFK5MmTbqnSxl7U6RQKKBSqXDx4kX09/cjPDwc27Ztw44dO5CdnT1Gkd9k\n48aNKC8vh0qlIiI+9hAR5xki4g5Ma2srZs2ahcrKSqc6pY0Fg4OD+OMf/4iPP/4YycnJEAgEmD17\nNgoLC5GXl2eThjW2yYsVdZPJNGwzm6XXNJvNqKyshJeX16jtaseazs5OtLe3IyMjw6radWNjIz7+\n+GOcOnUKHh4eSE9Px5w5c/DMM8+MyQKa9vZ2FBUVS4vi7gAADbJJREFUYc2aNdi4cSMR8bGHiDjP\nkDlxB0WtVuOJJ57A5s2biYCPwLFjx3Dw4EFcvnwZERER6OnpQUlJCb755husWrUKMTExnN97cnIy\nL0IpEAjg7+8Pf39/xMfHg6IoDAwMQCaTobW1dVg9WCwWj3hNdgzL2ebWGYZBQ0MDdDqd1QYuBoMB\nmzZtgkAgQE1NDdzc3FBbW4vS0lKYzWYbRH07q1atwu9+9zsMDg7y+rj/+7//C4lEglWrVgEA1qxZ\ng5CQkHHRz0KwL+Qk7oCYTCYsXLgQCxYswOuvv27vcBwStVoNd3f3EU+/rGMYW09vaGhAVlYWt5kt\nLCzMJvXXW+vBbm5uw+xN+/r60NzcjLS0NPj6+vJ+fVthMpm4bJC1C2P6+vpQVFSEhQsX4vXXX7dL\n9uHHH3/EoUOH8Pnnn+PYsWP4+OOPeTuJt7a2YtGiRbh06RJomkZSUhLOnz/vVP78YwQ5ifMMEXEH\ng2EYFBUVQSKRYPPmzfYO54HAbDbj4sWLnKgPDAwgPz8fUqkUBQUF8PX1tYmo6/V6yOVyyGQyyGQy\nCAQCxMXFITg4+L6d0OyFRqNBRUXFqAxcqqqq8NJLL2H9+vX42c9+xnOElrN69Wp88803cHV1hV6v\nh0qlwqJFi7Bz505eHn/evHn43e9+h56eHmzduhV/+ctfeHncBwzH/9A7GUTEHYxTp06hoKAAGRkZ\n3Gnlgw8+wCOPPGLnyB4cNBoNTp06heLiYpw4cQIikYhb4jJ16lRem8xYG1JfX1+Eh4cPc0Lz8/Pj\nTuqOYOxyK/39/WhsbBxV5uDQoUN4//33sXPnTqSnp/McofXwfRIHgH379qGsrAzd3d0oKioi39mR\nISLOM0TECeMahmHQ39+P0tJSlJaW4vz58wgPD+dS76mpqVanfgcHB1FVVTXiKZbdzMaKOkVRw5rk\n7LkDnPXAZ53jrLmpoWkaW7ZsQWlpKfbt24fg4GAbRGo9thBxo9GIjIwMmEwmNDQ02M04yMEhIs4z\nRMQJhCEwDIOmpiaUlJSgtLQUNTU1SEtL45rkLF1G0tXVhevXryMjI8OiFZoURQ1zkhMIBNwp3d/f\nf8xqyBRFoaamBkKh0OqGQL1ej//5n/+Bp6cnPvvsM6canxstL7/8MsRiMTZs2GDvUBwVIuI8Q0Sc\ncEeIKcbN1+DKlStcPb2vrw/Tpk1DYWEhZs2aBbFYPEzU2aY6vV6PtLQ0q0/URqORa5IbGBiAm5sb\nt5mNj3WhI2EwGHDt2jWEhYUNW8t7P/T09GDJkiV46qmn8NprrzlF3Z8vaJpGTk4Ovv32WyQlJdk7\nHEdl/Hwgxggi4oQ7Qkwxbkev1+P06dMoLi7G8ePHwTAMCgoKMGfOHERHR+Ptt9/Ge++9h4SEBF4F\njF0XKpfLh60LDQwM5MVrnDVwSU5OhkQiseoxrl69ipdffhm//e1v8fDDD486JmeiuroaCxcuxOOP\nP45PPvnE3uE4MkTEeYaIOGFEiCnGvWEYBgqFAkePHsXu3btx5MgRTJ06lWuSy8jIsEldlGEYqNVq\nTtT1ej38/f0RGBg4bLOYpXR1daGtrQ2ZmZlW3RAwDIMffvgBH330EXbt2oWUlJT7fgzCuIGIOM8Q\nsxfCiNjKFONBgq1b63Q6dHR0oLy8HEKhECUlJfj973+PiooKJCcnc/X0uLg4Xk7nAoEAvr6+8PX1\nRWxsLNckJ5PJ0NbWBpqmOdOZgICAO95IMAyDxsZGaLVa5ObmWpX6p2kaH330EcrKylBSUmL1KZ5A\nIFgHOYkTbsOWphgPImfPnkVmZuZtazhpmkZFRQVXT+/o6MCUKVMglUoxa9YsBAYG2qRmbDaboVQq\nIZPJoFQqIRQKh21mY1eHVlRUjMrARavV4pVXXkFwcDA2b97sULvZCQ4LOYnzDBFxwm3Y2hRjvGIw\nGHDmzBmUlJTg6NGjMBqNKCgogFQqxfTp063axW0JRqORS70PDAxAJBJBq9UiNjYWMTExVgl4V1cX\nFi9ejOeeew6/+MUvxlUDG2FUkA8KzxARJ9wVchK3HUqlEsePH0dxcTHKysrg7+/PrVrNzs62yay4\nTCZDXV0dQkJCoNVqodFo4OPjw3W+W7KZ7eLFi3j11VexadMmzJ07l/cYh3Ljxg0sWbIEPT09EAgE\nWL58OfEjd26IiPMMEXHCXSEiPjYwDIOOjg5uPv3y5ctITEzkRD0hIWFUs+IMw+DGjRvo7e1FZmYm\n1/zGMAwGBwe5k7rRaIS/vz+Xfh+aImcYBt999x22bNmCvXv3jskYVVdXF7q6upCTk4PBwUHk5ubi\nwIEDSE1Ntfm1CTaBiDjPEBEnEBwQmqZRU1PD1dNbW1uRk5ODwsJCFBYWIiQkxOIUNvtYAoEAkyZN\nuuvNAE3Tw0xnGIbBoUOHkJ2djatXr6KiogK7d++GWCzm66neF4899hhWrFiBefPm2eX6hFFDRJxn\niIgTHBqlUolly5ahsrISAoEA27Ztw/Tp0+0d1phjMplw7tw5lJSU4MiRI9BqtZgxYwakUikeeugh\n+Pj4jPjvWAOX0NBQREdH33ft2mw2Y/fu3dixYwe3gW3evHmYP38+cnJy+HhqFtPa2opZs2ZxG9UI\nTgkRcZ4hIk5waIqKilBQUIBly5bBaDRCq9Xa7RToSKhUKpw4cQLFxcU4ffo0vLy8uFN6bm4uRCIR\nzpw5A51Oh6ysLKtXYra3t2Px4sV46aWX8OKLL6KrqwtHjhxBe3s73nzzTZ6f1Z1Rq9WYPXs21qxZ\ng0WLFo3ZdQm8Q0ScZ4iIExyWgYEBZGdno7m5mXQ/3wWGYdDT04OSkhKUlJTg4sWL8PHxQV9fHz75\n5BPMnTvXqnr6uXPnsHLlSvz+97/H7NmzbRC5ZZhMJixcuBALFizA66+/brc4CLxAvsg8Q0Sc4LBc\nuXIFy5cvR2pqKq5evYrc3Fxs2bLFooUi4xWapvHOO+/g3LlzWLBgAU6fPo3GxkZkZ2dzm9lCQ0Pv\nelPEMAz27t2LL774Avv370d8fPwYPoPbYykqKoJEIsHmzZvtFgeBN4iI8wwRcYLDUl5ejvz8fJw+\nfRrTpk3DypUr4efnh/Xr19s7NIelrKwMBw8exPr167nTt9lsRnl5Odckp1KpMH36dEilUsycOXNY\nfZmiKLz33nuoq6vDrl27rN4jzhenTp1CQUEBMjIyuOfzwQcfkF3dzgsRcZ4hIk5wWLq7u5Gfn4/W\n1lYAwMmTJ7FhwwYcPHjQvoE5OWq1GqdOnUJxcTFOnjwJNzc3zJo1C/n5+fjTn/6E9PR0fPDBB2Qf\nNsEWEBHnGeKdTnBY2JWYdXV1SE5ORmlpKZkP5gEfHx88/PDDePjhh8EwDPr6+lBaWopNmzZh2rRp\n+PDDD0kPAoHgJJCTOMGhuXLlCteZPmHCBHz11VcICAiwd1gEAsE6yN0hzxARJxAIBMJYQUScZ6z3\ncSQQxhmbNm1CWloa0tPT8cwzz0Cv19s7JAKBMM4hIk6wigsXLiAzMxN6vR4ajQZpaWmorKy0d1g2\no6OjA59++inKy8tRWVkJiqKwd+9ee4dFIBDGOaSxjWAVU6ZMwaOPPoq3334bOp0Ozz33HNLT0+0d\nlk0xm83Q6XTcKs+IiAh7h0QgEMY5pCZOsBqj0YgpU6bAw8MDZWVlD/xI0pYtW7BmzRp4enpi/vz5\n2LVrl71DIhCcDVIT5xmSTidYjUwmg1qtxuDg4ANfH1YoFPj+++/R0tKCzs5OaDQa7Ny5095hEQiE\ncQ4RcYLV/Pd//zfWr1+PZ599Fr/5zW/sHY5NKSkpQXx8PIKDgyESibBo0SKUlZXZOyyH5fDhw0hO\nTkZiYiI2bNhg73AIhAcWUhMnWMWOHTsgEonwX//1X6AoCjNmzMCRI0cwZ84ce4dmE2JiYnD27Flo\ntVp4enqitLQUeXl59g7LIaEoCq+++iqKi4sRFRXF9U8Qox4CgX9ITZxAsJB3330X+/btg6urKyZP\nnoytW7fC3d3d3mE5HGfOnMHatWvx008/AQA+/PBDAMDq1avtGRbBMSA1cZ4hJ3ECwULWrVuHdevW\n2TsMh6ejowPR0dHcn6OionDu3Dk7RkQgPLiQmjiBQCAQCE4KEXECwUlYunQpQkJChs3jy+VyzJs3\nD0lJSZg3bx4UCoUdI7xJZGQkbty4wf25vb0dkZGRdoyIQHhwISJOIDgJzz//PA4fPjzs7zZs2IC5\nc+eioaEBc+fOdYhO8ClTpqChoQEtLS0wGo3Yu3cvHn30UXuHRSA8kBARJxCchFmzZkEikQz7u++/\n/x5FRUUAgKKiIhw4cMAeoQ3D1dUVf/jDH7BgwQKkpKTg6aefRlpamr3DIhAeSEh3OoHgRLS2tmLh\nwoWcT71YLIZSqQQAMAyDgIAA7s8EggNCutN5hpzECYQHBIFAAIGA/EYSCOMJIuIEghMTGhqKrq4u\nAEBXVxdCQkLsHBGBQBhLiIgTCE7Mo48+iq+//hoA8PXXX+Oxxx6zc0QEAmEsud+aOIFAsBMCgWAP\ngEIAQQB6ALwL4ACA/QBiAFwH8DTDMHJ7xUggEMYWIuIEAoFAIDgpJJ1OIBAIBIKTQkScQCAQCAQn\nhYg4gUAgEAhOChFxAoFAIBCcFCLiBAKBQCA4KUTECQQCgUBwUoiIEwgEAoHgpBARJxAIBALBSSEi\nTiAQCASCk/L/AVfDpHUGHVAhAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fe0b1318438>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(9, 6))\n",
    "ax = fig.gca(projection='3d')\n",
    "surf1 = ax.plot_surface(X, Y, Z, rstride=2, cstride=2,\n",
    "            cmap=mpl.cm.coolwarm, linewidth=0.5,\n",
    "            antialiased=True)\n",
    "surf2 = ax.plot_wireframe(X, Y, RZ, rstride=2, cstride=2,\n",
    "                          label='regression')\n",
    "ax.set_xlabel('x')\n",
    "ax.set_ylabel('y')\n",
    "ax.set_zlabel('f(x, y)')\n",
    "ax.legend()\n",
    "fig.colorbar(surf, shrink=0.5, aspect=5)\n",
    "# tag: sin_plot_3d_2\n",
    "# title: Higher dimension regression\n",
    "# size: 60"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Further Reading"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
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